Many of the material models used in the studies are rate-independent and linear hardening. For example, a
46Baskaran et al. / International Journal of Structural Changes in Solids 2(2010) 33-63Figure 13: Shot peening simulation using DEM3-D elastic-plastic analysis with strain-hardening is performed by Kyriacou (1996) with linear hardening models.Another example is the work by Guaglianoet al.(1999) who have performed a 3-D FEM simulation withkinematic hardening material model.Similarly, the simulations performed by Miaoet al.(2009) have usedrate-independent properties.A few unique examples are discussed here.Meguidet al.(2007) have included the strain-rate propertiesof Ti-6Al-4V alloy, by extrapolating from the static stress-strain curve.The approach by Al-Hassaniet al.(1999) has used Cowper-Symonds equation for predicting the stresses and strains for different strain rates dueto co-indentations.The material model does not segregate the strain, strain rate effects.Slimet al.(1995)use the elastic-plastic method proposed by Zarka and Inglebert to calculate RCS. This model consists of cyclicconstitutive relations that are developed by a family of internal parameters.The effect of temperature risedue to SP is coupled with mechanical effects through a thermo-elastic plastic model (Rouquetteet al., 2005).Fathallahet al.(1998, 1996) have used the material model by Guechichi and Khabou, while Barrallieret al.(2001) use Chabache model for engine disk components.The Chabache model is capable of handling bothisotropic and kinematic hardening through two internal variables and back stress.It is to be verified if themodel is applicable for large cold work occurring in the surface layers due to shot peening. Klemenzet al.(2009)also have performed using combined hardening visco-plastic (Chabache) model. Frijaet al.(2006) have used acombined damage model of Chabache and Lemaitre for Waspalloy. This model considers the surface defects dueto shot peening in the form of a damage parameter. Elastic-plastic material model with strain rates, dampingand deformable shot are considered to predict the stress field due to SP (Eltobgyet al., 2004).A comprehensive study on the effect of hardening models is conducted by Rouhaudet al.(2005). They havefound 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 hardeningis used. These models, however, do not consider strain-rates.The material models used include both rate-independent and rate-dependent models. As SP induces stresswaves, rate-dependent models are more appropriate. Besides, the material is likely become anisotropic due tocold work which also needs to be considered in modeling. The hardening of many materials is not purely isotropicor kinematic. Studies must include such combined hardening effects in future. To simulate relaxation, materialmodels that include cyclic stress-strain relations that are temperature and strain-rate dependent are required.