Many of the material models used in the studies are

Many of the material models used in the studies are rate-independent and linear hardening. For example, a

46 Baskaran et al. / International Journal of Structural Changes in Solids 2(2010) 33-63
Figure 13: Shot peening simulation using DEM
3-D elastic-plastic analysis with strain-hardening is performed by Kyriacou (1996) with linear hardening models.
Another example is the work by Guagliano et al. (1999) who have performed a 3-D FEM simulation with
kinematic hardening material model. Similarly, the simulations performed by Miao et al. (2009) have used
rate-independent properties.
A few unique examples are discussed here. Meguid et al. (2007) have included the strain-rate properties
of Ti-6Al-4V alloy, by extrapolating from the static stress-strain curve. The approach by Al-Hassani et al.
(1999) has used Cowper-Symonds equation for predicting the stresses and strains for different strain rates due
to co-indentations. The material model does not segregate the strain, strain rate effects. Slim et al. (1995)
use the elastic-plastic method proposed by Zarka and Inglebert to calculate RCS. This model consists of cyclic
constitutive relations that are developed by a family of internal parameters. The effect of temperature rise
due to SP is coupled with mechanical effects through a thermo-elastic plastic model (Rouquette et al. , 2005).
Fathallah et al. (1998, 1996) have used the material model by Guechichi and Khabou, while Barrallier et al.
(2001) use Chabache model for engine disk components. The Chabache model is capable of handling both
isotropic and kinematic hardening through two internal variables and back stress. It is to be verified if the
model is applicable for large cold work occurring in the surface layers due to shot peening. Klemenz et al. (2009)
also have performed using combined hardening visco-plastic (Chabache) model. Frija et al. (2006) have used a
combined damage model of Chabache and Lemaitre for Waspalloy. This model considers the surface defects due
to shot peening in the form of a damage parameter. Elastic-plastic material model with strain rates, damping
and deformable shot are considered to predict the stress field due to SP (Eltobgy et al. , 2004).
A comprehensive study on the effect of hardening models is conducted by Rouhaud et al. (2005). They have
found that isotropic hardening model gives better shape compared to kinematic and combined hardening models.
They have also found that the RCS continuously increases due to successive impacts when isotropic hardening
is used. These models, however, do not consider strain-rates.
The material models used include both rate-independent and rate-dependent models. As SP induces stress
waves, rate-dependent models are more appropriate. Besides, the material is likely become anisotropic due to
cold work which also needs to be considered in modeling. The hardening of many materials is not purely isotropic
or kinematic. Studies must include such combined hardening effects in future. To simulate relaxation, material
models that include cyclic stress-strain relations that are temperature and strain-rate dependent are required.