PREDICTION OF CHIP MORPHOLOGY IN ORTHOGONAL CUTTING BY MEANS OF A
2. BRIEF REMARKS ON THE NUMERICAL MODEL
The application of numerical modelling has encountered an always growing interest and diffusion in the field of metal forming (especially for 2D simulations) not only in the universities and other academic institutions, but also in the companies due to the satisfactory capability to properly represent the physical phenomenon. Of course, the effectiveness of the output results strongly depends on the input data In particular reliable information must be provided to the numerical model as far as the mechanical properties of the tools and the workpiece materials are concerned; as well the boundary conditions and the frictional phenomena at the interfaces among the tools and the workpiece require a suitable modelling.
Furthermore, when the deformation process involves material fracture (i.e. the insurgence and the propagation of a crack), the simulation model has to be able to represent the phenomena of shearing, defect formation and material separation. This is of course the case of the application here investigated, namely the chip formation mechanism. Here in fact a model simply based on a remeshing algorithm is not sufficient: this model could successfully predict continuous chip flow, but would lack when the study of wavy or saw tooth chip types wants to be addressed.
PREDICTION OF CHIP MORPHOLOGY IN ORTHOGONAL CUTTING 121
Thus, as above mentioned, a customized version of the commercial DEFORM 2D11 code was developed, able to simulate material breakage by deleting the mesh elements of the workpiece material when the damage value is higher than a defined critical value12"14• The modified code, as reported in figure l, differs from the original one in the remeshing module (which improves the mesh quality when it is too distorted and after the elements elimination), in the introduction of the damage criterion (which suggests where and when fracture begins) and finally in the subroutine which governs the elimination of the elements .
No
•
SIMULATION I
( + computation of the fracturing criterion) -.- - .
.--- ...
....--ELEMENTS . ..___
FRACTURE LIMIT
-~ TO ã__:::::..---~
'~ DELETE? ....--ã
..___..___ ~....--....--
. . Yes r: I
1
1ELEMENTS TO DELETE EXTRACTION OF THE I - -- ELEMENTS
T . _ _ DEI~E .I
l ELEMENTS DELE!ION 1 . . <lllc---- BORDER EXTRACTION
AND SMOOTHING
REMESHING
Figure 1. Algorithm for fracture simulation.
2.1 Implementation of Fracture Criterion
Ductile fracture is influenced by the deformation history applied on the workpiece, by the properties of the material (microstructure, surface conditions, presence ofmicrovoids) and finally by the process conditions (temperature, deformation rate, lubrication, friction). Such consideration demonstrates that the identification of a general and effective ductile fracture criterion able to predict fracture initiation for different stress states, strain rates and working conditions represents a very relevant aim to be pursued. A wide literature review shows that a very large number of ductile fracture criteria has been proposed up to now; the common
122 E. CERETTI ET Al.
hypothesis is that ductile fracture occurs when the maximum damage value in the workpiece exceeds a critical value or a so called critical damage value (Ccr)15•16•
f F(deformation history)dc = Ccr
Among the proposed criteria, the ones suggested by Oyane17, Cockroft and Latham18,
and McClintock19 are probably the most relevant. In some previous works, the authors proposed a new damage criterion based on the maximum shear stress calculation 14•
The basic assumption is that material breakage occurs in the primary deformation zone due to the shear stress (Figure 2). When the maximum shear stress is higher than a critical value tiim> which is the limit shear stress, fracture starts form the free surface of the chip. To implement the shear stress criterion, the value of maximum shear stress has to be calculated for each element of the mesh, by means of the following equations:
I
Unc:111 metal
Figure 2. Primary deformation zone and Maximum Shear Stress distribution.
All the elements satisfying the above described damage criterion are deleted, the workpiece is remeshed, the border is smoothed and a new calculation starts. Of course, the limit shear stress value has to be known. In this research the limit shear stress was assumed to be a material constant and was set on the basis of the ultimate shear stress. The latter was
PREDICTION OF CHIP MORPHOLOGY IN ORTHOGONAL CUTTING 123 measured by means of a set of experiments on an Hopkinson bar device, carried out on hat- shaped specimens20• The experiments were performed with temperature and strain rate conditions similar to the ones occurring during the cutting operations taken into account.
2.2 Model Implementation
A coupled thermal-mechanical analysis was performed to take into account both the temperature and the strain rate effects on the deformation mechanics. In order to model the workpiece material behavior, a set of data derived from literature was considered. ln particular, the flow stress rule proposed by Shirakashi, Maekawa and Usui21 for mild steel was utilized:
[MPa]
being:
Ao (T, & ) = 1394e-00011s r + 339e-0 0000184 [T-(94J+n.s1n(t11ooo))J'
The above flow stress model maintains its validity within the following variables range:
T = 293-970°K, e = 0,05-2, c = 10ã3 -104 sã1.
As far as the modelization of frictional phenomena at the tool-workpiece interface is concerned, a simple constant shear model, based on the law r = m . a/ Jj was utilized;
according to some previous investigations22•23
, the friction factor m was fixed equal to 0.82.
Finally the above mentioned limit shear stress value •inn was fixed equal to 640MPa.