Mechanical Properties of Engineered Materials 2008 Part 16 potx

time-However, it is important to note that the strain–time response in mostmaterials is not linear under constant stress ¼ o, i.e., creep conditions.Instead, most polymeric materials exh

time-Time-dependent creep deformation has also been observed in meric materials by viscous flow processes These can result in time-depen-dent elastic (viscoelastic) or time-dependent plastic (viscoplastic) processes.Such time-dependent flow can happen at temperatures above the so-calledglass transition temperature, Tg Time-dependent deformation may alsooccur in crystalline materials Depending on the crystal structure and tem-

poly-perature, these can give rise to stress-assisted movement of interstitials andvacancies, and an elastic deformation.

This chapter presents an introduction to time-dependent deformation

in crystalline and amorphous materials Time-dependent deformation/creep

of polymers is described along with the temperature dependence of mation in polymers Phenomenological approaches are then described forthe characterization of the different stages of creep deformation These arefollowed by an overview of the creep deformation mechanisms The creepmechanisms are summarized in deformation maps before discussing some

defor-FIGURE 15.1 Creep is important in four classes of design: (a) displacementlimited; (b) failure-limited; (c) relaxation limited; (d) buckling limited [FromAshby and Jones (1996) with permission from Butterworth-Heinemann.]

engineering approaches for creep design and the prediction of the creep lives

of engineering structures and components Finally, a brief introduction tosuperplasticity is then presented before concluding with an introduction totime-dependent fracture mechanics and the mechanisms of creep crackgrowth

15.2 CREEP AND VISCOELASTICITY IN POLYMERS

15.2.1 Introduction

In general, time-dependent deformation occurs in materials at temperaturesbetween 0.3 and 0.5 of Tm, the melting point (in K) In the case of polymericmaterials, which have relatively low melting points, considerable time-dependent deformation has been observed, even at room temperature.The resulting deformation in polymers exhibits much stronger dependence

on temperature and time, when compared to that in metallic and ceramicmaterials This is due largely to Van der Waals forces that exist betweenpolymers chains (Fig 1.8) Since the Van der Waals forces are relativelyweak, significant time-dependent deformation can occur by chain-slidingmechanisms (Chap 1)

15.2.2 Maxwell and Voigt Models

In general, the time-dependent deformation of polymers can be described

in terms of creep and stress relaxation, Fig 15.1(a) and (c) Creep is thetime-dependent deformation that occurs under constant stress conditions,Fig 15.1(a), while stress relaxation is a measure of the stress responseunder constant strain conditions, Fig 15.1(c) The underlying mechanics

of the time-dependent response of polymers will be described in this tion

sec-Time-independent deformation and relaxation in polymers can bemodeled using various combinations of springs and dashpots arranged inseries and/or parallel Time-independent elastic deformation can be modeledsolely by springs that respond instantaneously to applied stress, according toHooke’s law, Fig 15.2(a) This gives the initial elastic stress, o, as theproduct of Young’s modules, E, and the instantaneous elastic strain, "1,i.e., o¼ E"o, where"ois the instantaneous/initial strain Similarly, purelytime dependent strain–time response can be described by the viscousresponse of a dashpot This gives the dashpot time-dependent stress, d,

as the product of the viscosity,, and the strain rate, d"=dt [Fig 15.2(b),i.e., d ¼  d"=dt

The simplest of the spring–dashpot models are the so-called Maxwelland Voigt models, which are illustrated schematically in Fig 15.3(a) and (b),respectively.

Since the spring and the dashpot are in series, the stresses are equal inthe Maxwell model Hence, 1¼ 2¼ Taking the first derivative of strainwith respect to time, we can show from Eq (15.1) that

d"

dt¼d"1

dt þd"2

dt ¼1E

d

dt þ

where"1 ¼ ... acentury ago The extent of primary creep deformation is generally of interest

in the design of the hot sections of aeroengines and land-based gas turbines.However, the portion of the creep curve... dependence of therelaxation modulus is highly dependent on molecular weight and the extent

of cross-linking of the polymer chains This is illustrated inFig 15.12, whichshows the time dependence of. .. inpolymeric materials We will now turn our attention to the mechanismsand phenomenology of creep in metallic and ceramic materials with crystal-line and noncrystalline structures Creep in such materials