Astm stp 853 1985

KEY WORDS: planes, shear strains, multiaxial fatigue, definitions Several papers in this symposium refer to planes of maximum shear strain.. Any stress state having a principal stress r

MULTIAXIAL FATIGUE

1!

A symposium sponsored by ASTM Committees E-9 on Fatigue and E-24 on Fracture Testing San Francisco, CA, 15-17 Dec 1982

ASTIVI SPECIAL TECHNICAL PUBLICATION 853

K J Miller and M W Brown, University of Sheffield, editors

ASTM Publication Code Number (PCN) 04-853000-30

1916 Race Street, Pliiladelphia, PA 19103

Library of Congress Cataloging-in Publication Data

Multiaxial fatigue

(ASTM special teciinical publication; 853)

"ASTM publication code number (PCN) 04-853000-30."

Includes bibliographies and index

I Materials—Fatigue—Congresses 1 Miller, K J (Keith John) II Brown,

M W (Michael W.), 1947- III American Society for Testing and Materials

Com-mittee E-9 on Fatigue IV ASTM ComCom-mittee E-24 on Fracture Testing V Series TZ418.38.M85 1985 620.ri26 85-7376

ISBN 0-8031-0444-8

Copyright ® by AMERICAN SOCIETY FOR TESTING AND MATERIALS 1985

Library of Congress Catalog Card Number: 85-7376

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication

Printed in Ann Arbor, MI August IQ?.")

Foreword

This publication, Multiaxial Fatigue, contains papers presented at the

sym-posium on Biaxial/Multiaxial Fatigue which was held in San Francisco, fornia, 15-17 December 1982 The symposium was sponsored by ASTM Com-mittees E-9 on Fatigue and E-24 on Fracture Testing in cooperation with the American Society of Mechanical Engineers, the American Society for Metals, and the Society of Automotive Engineers K J Miller, University of Sheffield,

Cali-J R Ellis, Oak Ridge National Laboratory, and M W Brown, University of Sheffield, presided as symposium chairmen K J Miller and M W Brown are editors of this publication

Related ASTM Publications

Methods and Models for Predicting Fatigue Crack Growth Under Random ing, STP 748 (1981), 04-748000-30

Load-Fatigue Crack Growth Measurement and Data Analysis, STP 738 (1981), 738000-30

04-Effect of Load Variables on Fatigue Crack Initiation and Propagation, STP 714 (1980), 04-714000-30

Part-Through Crack Fatigue Life Prediction, STP 687 (1979), 04-687000-30 Fatigue Crack Growth Under Spectrum Loads, STP 595 (1976), 04-595000-30

ASTM Editorial Staff

Helen M Hoersch Janet R Schroeder Kathleen A Greene Bill Benzing

Requirements of a New Multiaxial Fatigue Testing Facility—

MICHAEL S FOUND, UPUL S FERNANDO, AND KEITH J MILLER 1 1

A Fatigue Test System for a Notched Shaft in Combined Bending

and Torsion—STEPHEN D DOWNING AND DALE R GALLIART 24

Multiaxial Fatigue Testing Machine for Polymers—

CHARLES C LAWRENCE 3 3

DEFORMATION BEHAVIOR AND THE STRESS ANALYSIS OF CRACKS

The Use of Anisotropic Yield Surfaces in Cyclic Plasticity—

STANLEY J HARVEY, AMRIT P TOOR, AND PAUL ADKIN 4 9

Transient and Stable Deformation Behavior Under Cyclic

Nonproportional Loading—DAVID L MCDOWELL AND

DARRELL F SOCIE 6 4

Crack Separation Energy Rates for Inclined Cracks in a Biaxial

Stress Field of an Elastic-Plastic Material—ALEX P KFOURI

A N D KEITH J M I L L E R 8 8

PROPAGATION OF LONG FATIGUE CRACKS

Fatigue Crack Initiation and Growth in a High-Strength Ductile

Steel Subject to In-Plane Biaxial Loading—

EDWARD W SMITH AND KENNETH J PASCOE 1 1 1

Mode I Fatigue Crack Growth Under Biaxial Stress at Room and

Elevated Temperature—MICHAEL W BROWN AND

KEITH J MILLER 1 3 5

Effect of Local Stress Biaxiality on the Behavior of Fatique Crack

Growth Test Specimens—DAVID RHODES AND JOHN C RADON 153

A/iT-Dependency of Fatigue Growth of Single and Mixed Mode

Cracks Under Biaxial Stresses—HIDEO KITAOAWA,

RYOJI YUUKL KEIICHIRO TOHGO, AND MASATO TANABE 164

Growth of Fatigue Cracks Under Combined Mode I and Mode II

L o a d s — G A O H U A , NET A T A L A G O K , M I C H A E L W B R O W N , A N D

KEITH J M I L L E R 1 8 4

Mode III Fatigue Crack Growth Under Combined Torsional and

Axial Loading—ROBERT O RITCHIE, FRANK A MCCHNTOCK,

ELMAR K T S C H E G G , AND HAMID NAYEB-HASHEMI 2 0 3

Fatigue Crack Path Behavior Under Polymodal Fatigue—

FRANgOIS HOURLIER, HUBERT D ' H O N D T , MICHEL TRUCHON, AND

ANDRE PINEAL 2 2 8

Discussion 248

Comments on Fatigue Crack Growth Under Mixed Modes I and III

and Pure Mode III Loading—LESLIE P POOK 249

FORMATION AND GROWTH OF SHORT CRACKS

Smooth Specimen Fatigue Lives and Microcrack Growth Modes in

Torsion—NICHOLAS J HURD AND PHILIP E IRVING 267

Crack Initiation Under Low-Cycle Multiaxial Fatigue—

BERNARD JACQUELIN, FRANgOIS HOURLIER, AND

ANDRE P I N E A U 2 8 5

Effect of Local Stress State on the Growth of Short Cracks—

BRIAN N LEIS, JALEES AHMAD, AND MELVIN F KANNINEN 3 1 4

The Role of Fretting in the Initiation and Early Growth of Fatigue

Cracks in Turbo-Generator Materials—TREVOR C LINDLEY

AND KEVIN J NIX 3 4 0

Fatigue of Steel Wire Under Combined Tensile and Shear Loading

Conditions—IGNAAS VERPOEST, BUDY D NOTOHARDIONO, AND

ETIENNE AERNOUDT 3 6 1

DAMAGE ACCUMULATION IN COMPOSITE MATERIALS

A Review of the Multiaxial Fatigue Testing of Fiber Reinforced

Plastics—MICHAEL S FOUND 3 8 1

Biaxial Fatigue of Glass Fiber Reinforced Polyester Resin—

JOHN C RADON AND CHRISTOPHER R WACHNICKI 3 9 6

Effect of Biaxial Loads on the Static and Fatigue Properties of

Composite Materials—DOUGLAS L JONES, P K POULOSE, AND

H LIEBOWITZ 413

LIFE PREDICTION TECHNIQUES FOR PLAIN AND NOTCHED COMPONENTS

Designing for High-Cycle Biaxial Fatigue Using Surface Strain

Records—DONALD L MCDIARMID 431

Biaxial/Torsional Fatigue of Turbine-Generator Rotor Steels—

ROY A WILLIAMS, RONALD J PLACEK, OLEG KLUFAS,

STEVEN L ADAMS, AND DAVID C GONYEA 4 4 0

Biaxial Fatigue of Inconel 718 Including Mean Stress Effects—

DARRELL F SOCIE, LINDA A WAILL, AND DENNIS F DITTMER 4 6 3

Discussion 479

Low Cycle Fatigue Properties of a 1045 Steel in Torsion—

GAIL E LEESE AND JODEAN MORROW 4 8 2

Fatigue Life Estimates for a Simple Notched Component Under

Biaxial Loading—JAMES W FASH, DARRELL F SOCIE, AND

DAVID L MCDOWELL 4 9 7

Fatigue Life Predictions for a Notched Shaft in Combined Bending

and Torsion—STEVEN M TIPTON AND DREW V NELSON 514

NONPROPORTIONAL LOADING EFFECTS

A Criterion for Fully Reversed Out-of-Phase Torsion and

Bending—SOON-BOK LEE 553

Fatigue Under Severe Nonproportional Loading—ERIC H JORDAN,

MICHAEL W BROWN, AND KEITH J MILLER 5 6 9

Fatigue Behavior of Cyclically Softening and Hardening Steels

Under Multiaxial Elastic-Plastic Deformation—

CETIN M SONSINO AND VATROSLAV ORUBISIC 5 8 6

Fatigue Under Out-of-Phase Biaxial Stresses of Different

Frequencies—DONALD L MCDIARMID 606

Effect of Changing Principal Stress Axes on Low-Cycle Fatigue

Life in Various Strain Wave Shapes at Elevated

Temperature—MASATERU OHNAMI, MASAO SAKANE, AND

NAOMI H A L M A D A 6 2 2

ELEVATED TEMPERATURE STUDIES

Biaxial Low-Cycle Fatigue of Cr-Mo-V Steel at SSS-'C By Use of

Triaxiality Factors—RICHARD H MARLOFF,

ROBERT L JOHNSON, AND WILLIAM K WILSON 6 3 7

Creep and Ageing Interactions in Biaxial Fatigue of Type 316

Stainless Steel—FATHY A KANDIL, KEITH J MILLER AND

MICHAEL W BROWN 6 5 1

A Metallographic Study of Multiaxial Creep-Fatigue Behavior in

316 Stainless Steel—E R DE LOS RIOS, F A KANDIL,

KEITH J MILLER, AND MICHAEL W BROWN 6 6 9

Damage Growth Under Nonproportional Loading—

DAVID R HAYHURST, FREDERICK A LECKIE, AND

DAVID MCDOWELL 6 8 8

The Determination and Interpretation of Thermally Promoted

Crack Initiation and Growth Data and Its Correlation with

Current Uniaxial Design Data—DAVID J MARSH AND

FRANK D W C H A R L E S W O R T H 7 0 0

SUMMARY

Summary 723 Index 731

Introduction

Multiaxial fatigue is a subject of concern to both engineers and research scientists In the eventuality of failure, fatigue lifetime is determined in the majority of cases by the applied multiaxial stress-strain state, whether generated

by multiple loading or the component geometry itself Thus multiaxial stresses should be taken into consideration by the designer, and it is important to note that material data generated in laboratories under constrained situations (for example, uniaxial loading or Mode I crack growth specimens) cannot be used

in practice without recourse to some multiaxial criterion The introduction of stresses on two or three axes in fatigue experiments, therefore, can provide valuable insight concerning both the micromechanisms of fatigue crack formation and growth and also the uses and limitation of multiaxial correlation factors The multiaxial behavior of metals has been studied throughout the twentieth century, and the engineers concern with the fatigue limit in the design of safe structures has led to a number of useful criteria which were developed prior to

1960, based on, for example, the pioneering work of Gough and Sines Two more recent developments associated with the finite life of structures are fracture mechanics and life prediction techniques for high-strain fatigue, both of which have required the development of additional criteria In these cases a knowledge

of the extent of plastic deformation is important since inelastic strains are used not only in low cycle fatigue analyses but also in advanced elastic-plastic fracture mechanics However, a number of problems remain to be solved, since fatigue cracks are invariably associated with notches or surface defects, and frequently experience aggressive environments

This volume presents a number of papers which were read at the International Symposium on Biaxial/Multiaxial Fatigue, sponsored by the American Society for Testing and Materials in collaboration with the American Society of Me-chanical Engineers, the American Society for Metals and the Society of Auto-motive Engineers The need for a conference was recognized in 1979 after preliminary discussions in Sheffield between the editors and European friends, but, because much new work in multiaxial fatigue had been funded by the Nuclear Regulatory Commission in Washington, it was thought proper to approach ASTM

to see if they would sponsor the event in the USA First contacts were made at the Bal Harbour meeting in Florida in 1980 via such people as Jane Wheeler and Don Mowbray The three day meeting, held in San Francisco in December

1982, led to many stimulating discussions among the delegates from several

2 MULTIAXIAL FATIGUE

countries, many of whom are actively involved in different aspects of the tiaxial problem It was apparent that a variety of approaches are now being developed, and this book summarizes the current state of the art in each area of concern

mul-The 38 papers have been divided into eight groups, of which the first two present the various tools available to the materials scientist, that is, laboratory testing followed by the characterization of cyclic deformation response and the stress analysis of cracks The importance of fatigue crack development, in terms

of both the propagation rate and the plane and direction of growth, is highlighted

by papers on mixed mode cracking and short cracks in metals The group of papers on composite materials illustrates other mechanisms of damage accu-mulation Life prediction techniques have been broadly based on crack devel-opment concepts, and new methods are compared with the older criteria and current design codes, showing that the new methods have much potential Two areas requiring more attention are nonproportional stressing and elevated tem-perature aspects such as creep fatigue Apart from these topics many other problems remain, but this volume shows that significant progress has been achieved towards predicting finite fatigue life behavior, and it should provide a useful aid

in interpreting failures and understanding the mechanics of fatigue

The success of the symposium and the production of this book would not have been possible without the hard work and support of the ASTM staff We would also like to thank our able cochairman, J R Ellis, and the invaluable assistance

of B N Leis in editorial matters subsequent to the symposium Both have given much time and generous advice The detailed work of the reviewers has greatly strengthened many papers presented here, and we appreciate the assistance of session chairman, the international group of experts who supported the sym-posium, ASTM committees E-9, and E-24 who sponsored the conference, and the staff of the Mechanical Engineering Department of the University of Shef-field

K J Miller

M W Brown

Department of Mechanical Engineering, versity of Sheffield, Sheffield, U.K sympos- ium chairmen and editors

Uni-General Discussion

Henry O Fuchs^

On the Definition of Planes of Maximum Shear Strain

REFERENCE: Fuchs, H O., "On the Definition of Planes of Maximum Shear Strain,"

Multiaxial Fatigue ASTM STP 853, K J Miller and M W Brown, Eds., American

Society for Testing and Materials, Philadelphia, 1985, pp 5-8

ABSTRACT: The concept of planes of strain is contrary to accepted definitions "Planes

of maximum shear strain" are defined as planes normal to the lines of maximum shear strain They are the same as planes of maximum shear stress The latter designation is unambiguous, simple, and in accord with accepted definitions It is proposed that the designation "planes of maximum shear stress" be used unless it can be shown that planes

of maximum shear strain are different from the former and more important as fatigue variables

KEY WORDS: planes, shear strains, multiaxial fatigue, definitions

Several papers in this symposium refer to planes of maximum shear strain This concept deserves careful examination

Strictly speaking strains are not related to planes but to directions, while stresses are related to the planes on which the forces are acting Stresses are defined as forces per unit area, for example, newtons per square metre (N/m^) For a given state of stress the direction of the area determines the stress and its components Stresses can not be seen nor measured directly

Strains are defined as relative changes in length of line segments (normal strains) or as changes in angle between two initially perpendicular lines (shear strains) They can be measured by strain gages, or seen by the change in shape and size of small circles or squares marked on surfaces

Figure 1 shows strains on the surface of a twisted circular bar This surface

is free of stress, but the amount of shear strain visible or measureable on it is greater than on any other plane in the bar However, this is not the plane of maximum shear strain to which the papers in this symposium refer

The maximum shearing stresses in the bar of Fig 1 occur on transverse and

on axial planes through a point on the surface These are also the "planes of maximum shear strain" to which many authors in this volume refer To define them in terms of strain we might say that they are two planes, each perpendicular

' Professor, Mechanical Engineering Department, Stanford University, Stanford, CA 94305

5

(a) Deformation of a square

{b) Deformation of another square

(c) Deformation of a circle

FIG 1—View of shear strains on a twisted shaft (Solid lines show final position, dashed lines

show original position.)

to one of the initial directions of the lines which between them show the maximum shear strain They will be called P-planes in this note

Note that sigma and epsilon are clearly positive or negative Gamma is an absolute value because the previously right angle between two lines becomes acute in two quadrants but obtuse in the two other quadrants when the strain gamma is applied An arbitrary sign convention can of course be defined when desired, but its definition must be explicit as it is not implied in the physical events Similarly an arbitrary sign convention is used to define the algebraic value of tau

The use of strains rather than stresses as fatigue criteria has obvious advantages when the deformations are largely plastic, as in low-cycle fatigue; this need not prevent identification of critical planes by reference to stresses, and identification

of crack growth direction by reference to stress direction Combined stress-strain criteria can be useful

The writer urges careful definition of the concepts used in discussion of

FUCHS ON DEFINITION OF PLANES 7 multiaxial fatigue He suggests that planes of stress and directions of maximum shear stress are much easier to define than planes and directions of maximum shear strain He proposes that planes and directions of shear stress be used rather

than "planes of maximum shear strain" at least until there is evidence that

P-planes can be different from and more critical than P-planes of maximum shear stress

In all cases which the writer was able to imagine the P-planes are also planes

of maximum shear stress To call them planes of maximum shear stress would have two advantages: It would avoid ambiguity and it would permit easy con-sideration of the direction of shear stress which is important for the direction of growth of cracks The direction of shear strain on the P-planes would need a special new definition

In connection with the directions of shear strains it is interesting to recall the now obsolete definition which von Mises used when he proposed the yield criterion known by his name.^ He used a shear stress space in which the principal shear stresses are the coordinates In such a space the Tresca yield criterion is

a cube, the von Mises criterion is a sphere, as in Fig 2 A similar method might

be required to define directions of shear strain

In some theories of multiaxial fatigue Mohr's circles of strain are used They are similar to Mohr's circles of stress, but the meaning of directions in them is

quite different: In the stress circle a radius at angle X from a principal stress

direction defines a plane at angle (X/2) from the plane of principal stress In

0°

-a

(a) For strains

(b) For stresses

FIG 3—Mohr's circles

^von Mises, R., Nachrichten der Gesellschaft der Wissenschaften, Gottingen,

Mathematisch-Physikalische Klasse, 1913, p 582

the strain circle one must consider diameters, not radii A diameter at angle Y

from a direction of principal normal strain defines two lines in the plane of two principal normal strains, one at angle (K/2) from the reference direction, the other

at (y/2 + 90°) The shear strain between those two lines is proportional to the vertical distance between the end points of that diameter, as shown in Fig 3

Multiaxial Fatigue Testing

Michael S Found,' Upul S Fernando.' and Keith J Miller^

Requirements of a New Multiaxial

Fatigue Testing Facility

REFERENCE: Found, M S., Fernando, U S., and Miller, K J., "Requirements of

a New Multiaxial Fatigue Testing Facility," Multiaxial Fatigue, ASTM STP 853, K J

Miller and M W Brown, Eds., American Society for Testing and Materials, Philadelphia,

1985, pp 11-23

Abstract: A new multiaxial fatigue testing facility is described It can strain a thin-walled

tubular specimen in three independently controlled loading modes by the use of torsion, axial load, and internal and external pressure Any stress state having a principal stress ratio between equibiaxial (\ = +1) and torsion (X = - 1) with any orientation of the maximum principal stress and the specimen axis can be chosen, with a maximum principal stress of 700 MN/m^ The significance of specimen geometry is examined in relation to multiaxial fatigue testing and the design of a suitable specimen is discussed Test data for

a ICr-Mo-V steel are presented to show the variation in multiaxial fatigue results for similar stress states obtained using different test systems and specimen geometries The possibility

of undertaking wider investigation of the effects of anisotrophy and cumulative damage is discussed

KEY WORDS: biaxial stresses, triaxial stresses, fatigue strength, high pressure, specimen

geometry, crack propagation, orientation, anisotropy, accumulative damage

Fatigue failures are still perhaps the commonest mode of failure among gineering components and structures despite the generation of a wealth of test data on the subject over many decades of research However most of these data have been obtained from laboratory experiments involving uniaxial loading con-ditions which are seldom present in practical engineering situations For example, components and structures found in power and chemical plants, such as pressure vessels and piping systems, aircraft structures, turbine blades, and drive shafts are subjected to multiaxial stress conditions during cyclic loading Many com-ponents are exposed to varying degrees of multiaxial strain especially at notches

en-or geometric discontinuities In en-order to apply these limited fatigue data to men-ore complex stress conditions attempts have been made to correlate multiaxial fatigue loading to an equivalent uniaxial fatigue loading condition as suggested in some

design codes [1,2]

It is now generally recognized that fatigue is concerned with the initiation and

'Lecturer, research assistant, and professor, respectively, Department of Mechanical Engineering, University of Sheffield, Sheffield, U.K

11

In both these cases the equivalent stress or strain may be similar, but the number

of cycles to cause failure will be quite different Brown and Miller [3] have

shown that under multiaxial loading conditions fatigue endurance is governed

by the maximum shear strain and the tensile strain normal to the plane of maximum shear Furthermore, the orientation of the surface to this plane is important since this defines either Type A or Type B cracks, which may propagate

in both Stage I and Stage II phases of crack growth The principal strain values

do not fully describe the fracture process under multiaxial fatigue since it is possible for similar strain conditions to give different fatigue lives A similar

approach has been used by Lohr and Ellison [4] to analyze cracks growing away

from the surface under in-phase loading conditions They have shown that fatigue crack growth rate is controlled by the maximum shear strain on planes driving the crack through the thickness and that the direct strain acting normal to the plane of maximum shear exerts a secondary modifying influence

Analysis of the results of available published data indicates that there is a

need for a multiaxial fatigue testing facility that will (a) permit the coverage of

all 3-D stress-strain states from pure torsion through the uniaxial state and plane

strain to the equibiaxial strain state, and (b) apply these 3-D stress-strain states

at any desired angle to the specimen axis This paper briefly reviews existing multiaxial fatigue systems and outlines the design requirements for a new testing facility presently being installed in the Department of Mechanical Engineering

at the University of Sheffield

Multiaxial Fatigue Systems

With the development of servohydraulic testing machines and associated loop control systems it is now possible to perform fatigue tests under complex stress-strain conditions by various means It is intended here to mention briefly some of these loading methods, a more comprehensive description being given

closed-by Refs 5-7 The test methods may be divided into two distinct categories; one

in which a single load system is used with specimens of variable geometry to obtain different biaxial stress states and the other in which the biaxial stresses are obtained by applying two or more loads to a specimen of fixed geometry Examples of the first category are cantilever bending, anticlastic bending, and bulge tests of flat plate specimens, pressurized tubes, and rotating disks The second category includes tension-torsion, tension-pressure, and tension-torsion-pressure of tubular specimens, uniaxial tests plus hydrostatic pressure and cru-

ciform specimen loading [5-7]

The first grouping, with the exception of the rotating disk experiment, requires

relatively simple test facilities together with suitable loading fixtures Features

of these methods are the ease of control of test parameters and of the measurement

of load and deflection However the major disadvantage is the problem of pretation of the results In addition to difficulties in determining the stress-strain distribution and the effect of stress gradients in each specimen geometry the use

inter-of a different geometry itself may influence the fatigue life due to variations in crack initiation and propagation behavior Therefore, these test methods are only suitable for evaluating similar stress-strain conditions

For the second grouping more expensive servohydraulic test systems are ally necessary since accurate control and load and strain measurements are re-quired With the exception of the tension-torsion test and the cruciform specimen, all these methods involve direct fluid pressure on the specimen which creates additional problems Fatigue endurance will be reduced due to the hydrowedge effect, and there may be also an environmental influence on crack initiation and propagation due to the fluid However these effects may be minimized by the use of a suitable protective sleeve For the complex geometry of the cruciform specimen, stress and strain measurement is difficult, and it is usually necessary

usu-to determine the stress-strain distribution in the test section by elastic-plastic finite element analysis

In order to compare the influence of both stress-strain state and the orientation

of the principal strains on fatigue behavior it is necessary to perform all tests over the complete range of biaxial stress states under similar conditions This highlights the need for a single test facility which will permit any stress-strain state with respect to any principal stress orientation to be obtained on the same

specimen geometry [8] A number of important requirements have been identified

[9] for an ideal multiaxial fatigue testing facility, and these are summarized next

1 Coverage of the complete range of biaxial/multiaxial stress states using a single specimen geometry

2 Control of the orientation of the principal stresses independent of the biaxial stress states and provision of a complete range of biaxial stress states with respect

to any principal orientation

3 Uniform stress-strain distribution over the gage length with minimum strain concentration at the end of the gage section

4 Stable specimen response for all stress states with a means of accurately determining stresses and strains in the gage area

5 Continuous controlling, monitoring, and recording of stresses and strains

in each principal direction

6 Flexibility in defining and controlling the fatigue load cycle with provision for the following functions:

(a) Choice of control mode; load, strain, or displacement

(b) Independent control over each principal load to permit in-phase or

out-of-phase loading

14 MULTIAXIAL FATIGUE

(c) Independent adjustments for mean value and amplitude of stress and strain in each principal direction

(d) Selection of cycle waveform and frequency

(e) Block programming facilities

7 Elevated temperature facility

8 Observation of the specimen during test

Two possible methods of obtaining most of these requirements were ered; namely, a modified cruciform specimen and a tubular specimen subjected

consid-to consid-torsion, axial load, and internal/external pressure Using an hexagonal shaped specimen with six loading arms it is possible to apply three independent axial loads to obtain the desired stress state With this specimen it is difficult to perform an accurate stress-strain analysis, and control of the loads in the indi-vidual arms is complex due to the constraints of the other arms However such

a test method permits observation of the specimen during testing and is suitable for elevated temperature work

The thin-walled tubular specimen is a simpler geometry enabling accurate stress-strain analysis even in the plastic range The torsion and axial loads can

be applied without mutual interaction, and the axial stress component due to pressurization can be monitored and easily corrected However it is not possible

to observe the specimen during testing, precise measurement of strain in the gage length can be difficult, and the maximum temperature is limited by the properties of the pressurizing medium Fatigue of thin-walled tubes is highly influenced by their machining history, especially grinding However, it is thought that by careful polishing of the gage length and honing of the bore this problem could be minimized Consideration of these facts indicated that a thin-walled tubular specimen would best meet our requirements

Multiaxial Fatigue Machine

The new multiaxial fatigue testing machine is capable of straining a walled tubular specimen in three independently controlled loading modes, namely, torsion, axial load, and internal and external pressure By applying axial load and internal/external pressure any biaxial stress-strain state with fixed principal directions can be produced The orientation of the principal stresses is rotated

thin-by superimposing a torsional load; hence, cracks may be generated on any required plane The loading systems are continuously and independently con-trolled so that fully reversed predetermined biaxial stresses may be applied in any direction on the specimen The use of pulsating external pressure as well

as internal pressure permits a greater combination of mean and alternating hoop stress to be explored, and the effect of mean stress on fatigue can be controlled

Therefore, any stress state having a principal stress ratio k between equibiaxial (X = 4-1) and pure shear (X = — 1) with any orientation a of the maximum

principal stress to the specimen axis can be chosen (Fig 1), with a maximum

FIG 1—Contours of various stress states that can be induced in a single specimen by the fatigue

machine

principal stress value of up to 700 MN/in^ For a limited range of stress states

it is possible to achieve a maximum principal stress of up to 1000 MN/m^ The rig comprises of a loading frame, pressure vessel, hydraulic power pack, and electronic controls The loading frame is a Schenck four column tension-torsion fatigue testing machine which provides axial and torsional loads of up

to ±400 kN and ±1 kNm, respectively The specimen is held between two identical chucks using two specimen holders The upper chuck is connected to the upper crosshead of the load frame via the upper sealing rod and the tension-torsion load cell The lower chuck is attached via the lower sealing rod to the tension-torsion actuator which is fixed to the base of the loading frame as shown

in Fig 2a The specimen and attached components are enclosed in a pressure vessel (Fig 2b) which is fixed to the lower crosshead and has the freedom to

move vertically along the specimen axis permitting specimen assembly to take place on the machine The pressure vessel end closures can be readily discon-nected, thus allowing the vessel to move down without affecting the dynamic seals on the upper and lower sealing rods, and hence avoiding any possible damage that could cause oil leakage

The loading frame and load carrying components are much stiffer than the specimen Therefore, the alignment of the upper sealing rod (that is, the load cell) to the lower sealing rod (that is, the actuator) is maintained even when the

16 MULTIAXIAL FATIGUE

o

z ui-J a.<9 CLUJO

specimen is not in the machine The alignment of the specimen to the loading axis is achieved by locating it on an internal mandrel which is permanently attached to the upper sealing rod The mandrel when engaged in the lower sealing rod acts as an additional safeguard to avoid introduction of misalignment of the specimen during assembly or testing The specimen holder consists of two parts The specimen is held in one part using a large nut which also transmits the axial load The second part, which is locked to the first part using a Morrison grip [70] and transmits pure torque to the specimen without introducing any significant bending loads to the gage area

The hydraulic circuit diagram for the test rig is shown in Fig 3 Two sifiers are employed to supply internal and external pressure to the system The external pressure and internal/external pressure difference are controlled inde-pendently from zero to 1700 bar by two servovalves located on the low pressure side of the intensifiers Thus, the hoop stress or pressure difference across the specimen can be accurately controlled by a given command signal Internal pressure is supplied to the specimen through the upper sealing rod and mandrel and sealed at the bore of the specimen The oil for the external pressure is fed directly to the pressure vessel Hence, there is no making or breaking of high pressure pipes during assembly of the specimen An automatic make up system

inten-is used so that any oil leakage can be replaced by injecting new oil into the system via a second pair of intensifiers while cycling continues Preliminary tests carried out to check the efficiency of the dynamic seals on the sealing rods indicated a very small leakage so that make up requirements should be relatively low These pressure systems are connected to the low pressure supply which provide the bulk amount of oil at tho start of a test A single hydraulic power pack capable of delivering oil at 80 L/min supplies the low pressure oil to the intensifiers and to the tension-torsion hydraulic circuits

The control system incorporates load, strain, and position control modes Each mode may be controlled independently for any waveform selected on the signal generator with different mean level, phase, hold time, and cycle time The axial load on the specimen may comprise of two components, one due to the load applied via the actuator and the other due to the end load exerted by the external pressure In order to be able to control the load on the specimen under these conditions a special feedback loop is incorporated so that the pressure load is interfaced with the axial load

Load measurements are obtained from the tension-torsion load cell and internal and external pressures are measured using ultrahigh pressure transducers Strain measurements are made on the gage length using two tranducers per mode, one measuring the displacement relative to the other fixed one, to counter any possible

pressure effects Chart recorders and x-y plotters are used to record load and

strain ranges as well as hysteresis loops

A set of safety trips able to detect overloads, failure of the oil supply or cooling water supply, and controlled emergency shut down circuit permit the machine

18 MULTIAXIAL FATIGUE

FIG Z—Schematic diagram of hydraulic circuits

to run unattended for long-term tests Safety screens are placed round the rig,

in case of high pressure leakages, and are interlocked with the machine controls

Specimen Geometry

Some of the requirements for specimen selection have been discussed earlier when a thin-walled tubular specimen was chosen for the test system One of the major advantages of using a tubular specimen for high-strain multiaxial fatigue studies is that it enables a fairly uniform stress-strain distribution to be obtained which can be determined accurately even in the plastic range [77] Furthermore, due to its simple geometry it is possible to manufacture the specimen to close

FIG 4a—Multiaxial fatigue specimen

tolerances at a reasonable cost Final selection of the specimen dimensions are

a compromise between the conflicting requirements of crack formation, stress distribution, and stability

The fatigue specimen designed for the test rig is shown in Fig 4a It has a

20 mm parallel gage section, a 22.3 mm outer diameter, and a 18 mm bore The ends of the gage length contain a 25 mm radius which gives the best possible stress-strain distribution over the gage area

Of the loading modes available axial load produces the most variable strain distribution The axial strain distribution in the gage section due to axial

stress-tension obtained by elastic-plastic finite element analysis is shown in Fig 4b

0.5

Inner Surface

C = l.l max stress yield stress

C= 1.03 to Yield

FIG 4b—Axial strain profiles due to axial tension

2 0 MULTIAXIAL FATIGUE

The analysis was performed for different specimen dimensions, and the results indicate that the influence of specimen shoulders, even with large fillet radii to reduce the stress concentration, produces significant strain variations over the gage length An increase in load produces more plastic strain at the center of the gage area, and, at high strains, fatigue cracks are expected to initiate at the bore in the region of maximum strain At low strain levels the stress concentration

at the fillets is more effective, and cracks are likely to initiate at both fillets and the center of the gage area Propagation of the cracks at the fillets will be localized and be inhibited by the high-strain gradient at these regions, and fatigue failure

is more likely to occur at the center of the gage area When subjected to torsion

or pressure the strain distribution is not significantly modified with increasing load For torsional loading cracks are expected to initiate at the outer surface while under pressure cracks should initiate at the bore

The ratio of internal to external diameters of the gage area is important, since

an increase in the ratio leads to a thicker wall section which in turn increases the resistance to buckling under compression Furthermore, the thicker walls minimizes errors caused by possible eccentricity of the specimen and allows

more material for propagation of Stage II Type B cracks It is reported [12] that

during high-strain torsional cyclic loading tubular specimens accumulate plastic strain in the axial direction This effect is more pronounced in thin-walled spec-imens and thus favors the use of a thicker tube for the specimens The major disadvantage of using a thicker tube is that it requires very high pressures to obtain substantial hoop strains which causes practical difficulties in designing the rig and increases the hazards of testing For the specimen just described the diameter ratio is about 0.8 for which thickness effects on fatigue life are not too significant and the specimen is sufficiently stiff to obtain fatigue lives of the order of 500 cycles without causing instability in compression

Discussion

In recent years many multiaxial fatigue tests have been conducted on a variety

of materials using different test systems and specimen geometries, and often the results are difficult to interpret and compare However, some results obtained for ICr-Mo-V steel have been well documented and have been recently analyzed

by Brown [13] He compared the results obtained from tension-torsion [14], tension-pressure [15], and plate bending [16] tests at room temperature per-

formed on the same material Brown replotted the results at two lives on the F-plane as shown in Fig 5 The tension-torsion data correspond to Type A cracks and the tension-pressure and plate bending results to Type B cracks with the uniaxial test separating the two types Figure 5 shows that the Type B cracks

(dashed line) are more damaging than the Type A cracks (solid line) leading to

lower fatigue strengths The plate bending (dotted line) appears to extend the

Type B fatigue life probably because the cracks propagating into the specimen meet a reducing stress gradient compared with a more uniform stress in the

tension-torsion test {solid line) The uniaxial test data also highlight differences

between tension-pressure and tension-torsion tests The former, which may be influenced by an oil environment, employed a thin-walled tube while the latter used a thick-walled tube and gave a higher strength

From the foregoing it can be readily seen that trying to understand multiaxial fatigue behavior under similar stress states using different test systems and spec-imen geometries is fraught with difficulties With the multiaxial fatigue testing facility previously described it will be possible to examine the response of a single specimen geometry to a given stress state in several different ways For example, examination of the vertical line drawn through the stress ratio X = 0

in Fig 1 indicates that many combinations of 3 and 7 will give the desired stress ratio; for example, 3 = 0"/ = 0, P = 1 7 = ± 1 , and 7 = 0 3 = ±t» For stress ratios - 1 < X < 0 cracks will propagate along the surface (Type A) of the specimen and for stress ratios 0 s X, s + 1 away from the surface (Type B) The fatigue machine thus permits the possibility of initiating a crack on one plane and propagating it along another plane Therefore, it is possible to study the hydrowedge effect due to oil pressure on the growth of short cracks by separating out the initiation and propagation stages in the tension-torsion regime For example, this can be examined at stress ratio X = - 1 by applying pure torsion (P = 0 7 = ± M ) , pressure and axial load (P = - I 7 = 0), and other value for 7 with p = - 1 For different values of X different pressures are required

Most if not all engineering materials are nonisotropic in their behavior isotropy may be introduced during manufacture by rolling, forging, or extrusion

An-or during cyclic defAn-ormation which produces a specifically An-orientated graphic texture Thus the fracture resistance for a particular loading mode may

metallo-be increased by texturing a material in a preferred direction A crack may still propagate on the same plane and in the same direction but at a different rate if the orientation of the specimen relative to the texture is changed or if the cyclic

22

deformation response changes The fatigue machine will enable tests to be formed on anisotropic materials for any selected stress state aligned with any given direction in the material In order to separate out deformation and fracture response from the influence of specimen geometry and loading mode further tests can be performed on specimens taken from a block of material at other orientations followed by testing at the identical stress state and material orien-tation previously selected

per-Engineering components that do not contain inherent defects and operate at stress levels near to the fatigue limit, spend most of their life in the initiation and short growth regimes Therefore, the understanding of the accumulation of damage in the initiation phase is of great importance The well known Palgrem-Miner rule I ^ r : = 1 I for the summation of damage assumes that damage accumulates in a linear manner independent of the sequence of loading and is based on the results of uniaxial tests With the fatigue machine it will be possible

to perform cumulative damage fatigue tests in order to explore damage summation under multiaxial stress-strain conditions which will be more applicable for use

in design codes It will be also possible to undertake cumulative damage studies for situations in which defects can be orientated in any desired plane relative to the 3-D stress field

Acknowledgments

The authors wish to acknowledge the funding of this project by the Science and Engineering Research Council U S Fernando wishes to acknowledge the financial support given by UNESCO and The Royal Commission for the Ex-hibition of 1851

The authors wish to thank Dr M W Brown for his encouragement and advice and Mr M R Goldthorpe for the use of his elastic-plastic finite-element pro-gram

References

[/] ASME Boiler and Pressure Vessel Code Section VIII Division 2, ASME, New York, 1980, Appendix 5, pp 475-483

[2] BS 5500, Specification for Unfired Fusion Welded Pressure Vessels, BSI, London, 1982, Appendix C, pp C1-C7

[3] Brown, M W and Miller, K J., Proceedings, Institution of Mechanical Engineers, Vol

[6] Andrews, J M H and Ellison, E G., Journal of Strain Analysis, Vol 8, No 3, 1973, pp

168-175

[7] Brown, M W., Proceedings, Conference on Measurement of High Temperature

Mechani-cal Properties of Materials, Chapter 12, National PhysiMechani-cal Laboratory, U.K., 1981

[5] Hsu, T C , Proceedings, Institution of Mechanical Engineers, Vol 180, 1965, pp 269-278

[9] Fernando, U S., "A New Machine for Multiaxial Fatigue Testing," M Eng thesis

Uni-versity of Sheffield, U.K., 1982

[10] Morrison, J L M., Proceedings, Institution of Mechanical Engineers, Vol 142, 1939, p 203 [II] Brown, M W., Journal of Strain Analysis, Vol 13, No 1, 1978, pp 23-28

[12] Miller, K J and Chandler, D C , Proceedings, Institution of Mechanical Engineers, Vol

[16] Adams, W R., "Uniaxial and Biaxial Low Cycle Fatigue Behaviour under Isothermal and

Temperature Cycling Conditions," Ph.D thesis University of Nottingham, U.K., 1972

Stephen D Downing^ and Dale R Galliart^

A Fatigue Test System for a Notched Shaft in Combined Bending and Torsion

REFERENCE: Downing, S D and Galliart, D R., "A Fatigue Test System for a

Notched Shaft in Combined Bending and Torsion," Multiaxial Fatigue, ASTM STP

853, K J Miller and M W Brown, Eds., American Society for Testing and Materials,

Philadelphia, 1985, pp 24-32

ABSTRACT: This paper describes the design of a two-channel test system that can generate

combinations of torque and bending on a round notched specimen The test frame consists

of a specially designed set of hardware for the size and shape of the SAE Fatigue Design and Evaluation Committee's round specimen The two RAM computer-controlled hydraulic closed loop system provides independent control for each RAM Load cells and stroke transducers are mounted in-line to provide signals for control and data processing In addition to a description of the hardware, this paper defines the software that is used to control the system and perform data analysis on five channels of data The data consist

of the two channels of load and three channels of strain from a rectangular rosette An ultrasonic surface wave technique is used to detect a crack of defined size and automatically halt the test

KEY WORDS: biaxial fatigue, test system, notched shaft, computer controlled, ultrasonic,

bending, torsion, rosette strain gage

The test system described in this paper is the result of an effort in support of the Society of Automotive Engineers Fatigue Design and Evaluation Committee This committee set out to extend its fatigue life activities by initiating a biaxial fatigue test program Because the participants represent the ground vehicle in-dustry, a notched shaft under combined bending and torsional loading was chosen

as a typical component To satisfy the needs of this program, a test system that could perform the following tasks was developed:

1 The system should be capable of providing any combination of in-phase and out-of-phase bending and torsional loads Preliminary calculations deter-mined that the system should be capable of 7000 Nm of bending and torsion for the selected specimen and material Specimen dimensions are given in Fig 1 The selected material was normalized 1045 steel (430 MPa yield strength, 620 MPa ultimate strength, and 55% reduction in area)

'Senior research engineer and manager of Metals Research, respectively The Technical Center, Deere and Company, Moline, IL 61265

24

FIG 1—SAE notched shaft specimen

2 The system should be capable of duplicating variable amplitude measured

field loads or "simulated" field loads

3 The system should record sufficient data during the test cycle for analysis

of fatigue life prediction theories These were resolved to be life to crack initiation (which is defined in a later section), life to final fracture, the applied loads, and the surface strain tensor at the expected crack initiation site

4 A load controlled test system would appropriately simulate the loading of this specimen

The simple loading scheme illustrated by Fig 2 was considered appropriate for these requirements Two linear actuators controlled by a single computer is

an effective method of generating any combination of bending and torque with known phase relationships

Mechanical Hardware

The load frame configuration was designed to meet the following criteria:

1 Sufficient fatigue strength for the specimen size and material

2 Accommodate two hydraulic actuators (44 KN maximum load and 150

mm stroke) with in-line load cells

3 Convenient access to the specimen by the operator

The final load frame design was a welded steel frame outlined in Fig 3 The bending and torsional moment arms are 155 and 203 mm, respectively

The specimen gripping system is shown in Fig 4 The large end of the specimen is simply clamped between two machined steel blocks The small end

is gripped by a heat-treated wedge collet In preliminary tests, no collet slippage occurred until approximately 3000 Nm of torque was applied Subsequent to the development of this collet, a commercially available version with greater gripping capacity was found The attachment at the load cell was by monoball studs Likewise, the lower end of the ram was attached to the base plate by monoball

TOP OF LOAD FRAME

LOADING ARM

COLLET

TO LOAD CELLS

FIG 4—Specimen gripping system

fixtures to allow for movement in two directions A photograph of the specimen mounted in the load frame is shown in Fig 5

Instrumentation

The instrumentation system is comprised mainly of standard equipment able to most of the test participants Figure 6 shows a block diagram of the instrumentation system components which are outlined below

avail-Servohydraulic Control

Each hydraulic actuator is load controlled by separate servohydraulic test consoles These units condition the command and transducer signals and provide closed-loop control of the servovalves so that the desired forces are applied to the hydraulic actuators

Computer and Interfaces

A 16 bit minicomputer with 28 k words of random access memory and dual floppy disk drives communicates with hydraulic equipment through a hardware

2 8 MULTIAXIAL FATIGUE

FIG, 5—Specimen mounted in load frame

interface This interface is equipped with two 12 bit D/A converters and eight

12 bit A/D converters Peripherals include a graphics display terminal, a digital plotter, and a hardcopy unit

Crack Detection

In order to detect small cracks with minimum operator intervention, an sonic surface wave transducer was used This transducer transmits an ultrasonic sound wave along the surface of the specimen and receives reflected waves from certain reference points as well as crack interfaces The path of the surface wave

ultra-is illustrated in the upper portion of Fig 7 The bottom half shows a representative output from the oscillograph of the ultrasonic instrument Three blips corre-sponding to reflected waves from Points A, B, and C are seen At Point A, the transmitted wave from the transducer strikes the specimen Point C is a discon-

TERMINAL DEC PDP-11/04

MINICOMPUTER PLOTTER

^ARD COPY]

FLOPPY DISCS

DIGITAL INTERFACE

un

CONTROLLER

STRAIN GAGE COND

ULTRA SONIC DETECT

FIG 6—Block diagram of instrumentation system

tinuity at the top of the specimen radius An initiated crack would cause an intermediate blip at Point B The ultrasonic instrument is capable of turning on

an alarm if the height of this blip exceeds a presettable limit

The procedure for calibrating the ultrasonic instrumentation is given as follows:

1 Adjust the gain and attenuation of the ultrasonic unit so that the alarm circuit is activated by a machined 0.7 mm notch on a special calibration specimen This depth was chosen as the approximate size of crack in the small, round, smooth polished specimens which are used to obtain material properties

\

\SURFACE WAVE

FIG 7—Path of ultrasonic surface wave

3 0 MULTIAXIAL FATIGUE

2 Transfer the transducer from the calibration specimen to the test specimen

3 The fatigue computer program checks the voltage of the alarm circuit which

is normally zero volts When activated, the output is a zero-to-four volt square wave

4 Upon detection of this alarm signal, the program will print the number of current test cycles and stop the test for visual inspection

Software

The following discussion is limited to the software for conducting constant amplitude fatigue tests under combined bending and torsion and for analyzing the rosette strain gage data resulting from these tests Care was taken to develop

a simple scheme for inputing test parameters and an effective disk filing system

so that data may be completely analyzed after the test is over

Software for running the test must be able to do the following;

1 Output proper command signals to the servoamplifiers

2 Record loads and strains at various times during the tests and store on disk

3 Monitor certain variables as conditions for test shutdown

The scheme chosen for inputing bending and torsion control parameters is described next End levels are input for five points in a test cycle for both bending and torque The signal to be output through the D/A converters to the individual servoamplifiers is calculated from these end levels Output waveforms may be configured as either ramps or haversines, and the number of individual steps making up these waveforms (up to lOO/cycle) is input by the test operator

7 6 mm TYP

RECTANGULAR ROSETTE (BLH FAER 03B-12-56)

FIG 8—Rosette strain gage orientation

During the first part of the fatigue test, a rosette strain gage (Fig 8) is monitored, and the following scheme for data acquisition is used:

1 The first 100 peaks and valleys of normal and shear strains are detected and stored to help characterize early material hardening or softening or both

2 A two-cycle burst of load and strain data is collected and stored on a disk

at specified cycle counts (1, 501, 1001, 5001, 10 001, etc.) The number of simultaneous data scans/cycle (up to 100) is set by the test operator at startup After the strains have stabilized (or the gage failed), the strain gage is removed and the ultrasonic crack detector is installed The program now monitors the alarm circuitry of the ultrasonic instrument and performs a test shutdown when

a crack is detected At this point, the crack detector is removed, and the test is run to specimen fracture The stroke transducers are continously monitored for large changes in specimen compliance, thus alerting the test operator to the eventuality of fracture Whenever a test shutdown occurs (either manually or by failure criteria), the number of accumulated cycles is output and automatically copied

Another computer program was written to fully analyze the load and strain data previously stored on a disk by the test program Most of the program options are involved with characterizing the strain tensor at the root of the specimen notch

Test Procedure

The following shows the typical sequence of events needed to run constant amplitude biaxial fatigue tests with this system

1 Gage specimen

2 Install specimen in load frame

3 Run single cycle test

4 Run fatigue test to strain stability

5 Remove gage and install crack detector

6 Run test to crack initiation

7 Remove crack detector

8 Take replica and restart test

9 Run test to final fracture

10 Analyze strain data

Discussion

The described system meets the defined objectives for performing constant amplitude load controlled fatigue tests in combined bending and torsion The simple, two actuator scheme for applying loads, although theoretically incapable

of pure torque, provides an economical means for generating combined bending