Material Behavior Description for a Large Range of Strain Rates from Low to High Temperatures: Application to High Strength Steel

Abstract

Current needs in the design and optimization of complex protective structures lead to the development of more accurate numerical modelling of impact loadings. The aim of developing such a tool is to be able to predict the protection performance of structures using fewer experiments. Considering only the numerical approach, the most important issue to have a reliable simulation is to focus on the material behavior description in terms of constitutive relations and failure model for high strain rates, large field of temperatures and complex stress states. In this context, the present study deals with the dynamic thermo-mechanical behavior of a high strength steel (HSS) close to the Mars ® 190 (Industeel France, Le Creusot, France). For the considered application, the material can undergo both quasi-static and dynamic loadings. Thus, the studied strain rate range is varying from 10 −3 -10 4 s −1 . Due to the fast loading time, the local temperature increase during dynamic loading induces a thermal softening. The temperature sensitivity has been studied up to 473 K under quasi-static and dynamic conditions. Low temperature measurements (lower than the room temperature) are also reported in term of σ − ε|˙ε ,T curves. Experimental results are then used to identify the parameters of several constitutive relations, such as the model developed initially by Johnson and Cook; Voyiadjis and Abed; and Rusinek and Klepaczko respectively termed Johnson-Cook (JC), Voyiadjis-Abed (VA), and Rusinek-Klepaczko (RK). Finally, comparisons between experimental results and model predictions are reported and compared.Nevertheless, in numerical models, constitutive relations are used to describe the material mechanical behavior and consequently have a strong influence on interpretation of the results. Therefore, reliability of these models is essential. These material constitutive relations usually represent the equivalent plastic stress σ of a material as a function of the equivalent plastic strain ε p , strain ratė ε p , and temperature T. Many relations have been developed through recent decades and are still under consideration. One can distinguish two main types of constitutive relations. The first ones are phenomenological, as they do not take into account any physical phenomenon and are only based on experimental observations. These relations have the main advantage of having a low number of constants. Nevertheless, their validity is reduced to a limited range of conditions in term of strain rate and temperature. A well-known and widely implemented in finite element (FE) codes is the Johnson-Cook constitutive model [4]. Johnson and Cook used a phenomenological model that is widely used in most applications for predicting the behavior of the flow stress at different strain rates and temperatures. In this model, the strain rate and temperature effects on the flow stress are uncoupled which implies that the strain rate sensitivity is independent of temperature which is in contrast to that observed by most metals. It is an empirical e...

Investigations on Mechanical Properties of Lattice Structures with Different Values of Relative Density Made from 316L by Selective Laser Melting (SLM)

“…Furthermore, in commonly available CAE systems, there are few versions of modified J-C constitutive material models that enable the consideration of additional material failure criteria caused by damage mechanisms [86][87][88]. Nevertheless, the J-C constitutive relations also have some drawbacks, which have caused newer, more sophisticated and more accurate descriptions to be formulated (e.g., Rusinek-Klepaczko) [89][90][91][92].…”

Characterization of the Mechanical Behavior of a Lead Alloy, from Quasi-Static to Dynamic Loading for a Wide Range of Temperatures

“…The temperature tests are made in a furnace which has been specifically designed for SHPB tests. The scheme representing its operating mode is given in Figure 11 [11][12][13][14][15][16][17]. The extremities of the two bars are initially heated to the desired temperature during 30 min.…”

“…Figure 11. Schema of the oven used for the test using SHPB at high temperatures [11]. Tables 9 and 10.…”

“…Moreover, even if the mechanical characterization of metals like steel or aluminum is well mastered [11], the particularly soft mechanical behavior of lead can pose difficulties either for mechanical testing or production of specimens. Indeed, these latter are extracted by machining of the small caliber ammunitions which is a non-straightforward procedure.…”

A physically based constitutive model for dynamic strain aging in Inconel 718 alloy at a wide range of temperatures and strain rates

“…The profound discussion about these parameters is provided in [17]. Meanwhile, the logarithmic plastic strain rate is replaced with the normal plastic strain rate, lṅ̇0 →̇̇0, based on [27] in order to acquire a better agreement with the experimental data. Eq.…”