Modelling, identification and application of phenomenological constitutive laws over a large strain rate and temperature range

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. a b s t r a c t A review of the different phenomenological thermo-viscoplastic constitutive models often applied to forging and machining processes is presented. Several of the most common models have been identified using a large experimental database (Hor et al., 2013). The latter consists of the tests were done in compression on cylindrical shaped specimens and in shear using hat-shaped specimens. The comparison between these different models is shown that the group of decoupled empirical constitutive models (e.g. the Johnson and Cook (1983) model), despite their simple identification procedures, are relatively limited, especially over a large range of strain rates and temperatures. Recent studies have led to the proposal of coupled empirical models. Three models in this class have also been studied. The Lurdos (2008) model shows the best accuracy but requires a large experimental database to identify its high number of parameters. After this comparison, a constitutive equation is proposed by modifying the TANH model (Calamaz et al., 2010). Coupling between the effects of strain rate and temperature is introduced. This model is easier to identify and does not require knowledge of the saturation stress. Compared to other models, it better reproduces the experimental results especially in the semi-hot and hot domains. In order to study real machining conditions, an orthogonal cutting tests is considered. The comparison between experimental test results and numerical simulations conducted using the previously identified constitutive models shows that the decoupled empirical models are not capable of reproducing the experimental observations. However, the coupled constitutive models, that take into account softening, improve the accuracy of these simulations.

Advances in material and friction data for modelling of metal machining

“…Recently, a similar approach was used by Hor et al [112] to model the constitutive behaviour of three steels for use in machining simulations. Although not physically-based, the modified J-C model has been shown to work well for simulating segmented chip formation in cutting of low thermal diffusivity metals such as titanium and nickel base alloys [219].…”

“…The dependence of the accuracy of machining simulations on the test method and the associated loading conditions can be seen from the work of Hor et al [112], where a J-C model fitted with dynamic shear test data yielded peak temperatures closer to the experimental value than a model fitted with dynamic compression data. Even though the stress state in metal cutting is multiaxial, acceptable predictions (<10-15% error) of the forces, shear angle, and deformed chip thickness can be obtained from constitutive equations fit to uniaxial flow stress data (mostly from quasi-static and/or dynamic compression tests).…”

“…Even though the stress state in metal cutting is multiaxial, acceptable predictions (<10-15% error) of the forces, shear angle, and deformed chip thickness can be obtained from constitutive equations fit to uniaxial flow stress data (mostly from quasi-static and/or dynamic compression tests). Hor et al's [112] results also suggest that the primary deformation mode (compression vs. shear) in the materials test may be important for accurate prediction of quantities such as temperatures, strains, etc.…”

“…The choice of a constitutive model can impact the accuracy of machining simulations, as discussed by a number of authors [41,211,112,103,121,209,81,52,1]. Fig.…”

“…Reasons for the non-uniqueness of the model parameters include the nonlinear optimization method used to determine their values [172], the type of flow stress data used to fit the model (e.g. compression vs. shear) [112,111], and the ranges of strains, strain rates, and temperatures produced in the flow stress determination tests. For a given constitutive model, a detailed sensitivity analysis and validation against experimental data, similar to that reported by Childs [51], is necessary to identify the model parameter values that yield physically meaningful results.…”