Papers by Keyword: Constitutive Modeling

Abstract: Leather is a fiber-reinforced material with a more concentrated fiber distribution in three dimensions perpendicular to the tangential plane than in-plane. The asymmetric dispersion of fibers can have a significant effect on the mechanical properties of natural leather. The transverse isotropic constitutive model is unable to accurately describe the anisotropy of natural leather. Accordingly, we have devised a novel anisotropic theoretical framework that incorporates asymmetric fiber dispersion, with the objective of accurately characterizing the mechanical behavior of anisotropy with asymmetric fiber distribution. Our approach entails the incorporation of the Yeoh model into the theoretical framework, as well as the introduction of a specific anisotropy term within the strain energy function, with the objective of describing the nonlinear properties. By fitting the theoretical results of the model to tensile test data of natural leather specimens, the structural and material parameters were determined. We provided specific stress tensors to enable finite element analysis. Our finite element analysis investigates the effect of asymmetric fiber dispersion on the mechanical response under uniaxial and biaxial stretching. By simulating the tensile behavior of natural leather specimens under different tensile angles, we observe a non-homogeneous stress distribution and non-homogeneous deformation due to fiber families under fixed stretching. This theoretical framework based on a continuum model provides a theoretical reference for describing the mechanical properties of leather materials with asymmetric fiber dispersion.

Abstract: An experimental characterization of the austempered ductile iron ISO 17804/JS/1050-6/S was performed carrying out tensile tests under different strain rates, temperatures and stress triaxiality levels. Then, composing a yield function surface, a hardening relation, and a damage criterion, a constitutive model was developed to describe the salient features of the observed macroscopic response. In particular, the Mohr-Coulomb yield function was selected to account for the pressure effect observed on the yield surface. A new hardening relation was proposed in order to account for both strain rate and temperature effects. The Bonora’s damage model, developed in the framework of the continuum damage mechanics, was adopted to capture the failure condition under different stress triaxiality levels. The damage model was appropriately modified to account for the effect of strain rate and temperature on the failure strain.

Abstract: The hot compressive deformation behaviors of ZHMn34-2-2-1 manganese brass are investigated on Thermecmastor-Z thermal simulator over wide processing domain of temperatures (923K-1073K) and strain rates (0.01s^-1-10s^-1). The true stress-strain curves exhibit a single peak stress, after which the stress monotonously decreases until a steady state stress occurs, indicating a typical dynamic recrystallization. A revised constitutive model coupling flow stress with strain, strain rate and deformation temperature is established with the material constants expressed by polynomial fitting of strain. Moreover, better prediction ability of the constitutive model is achieved by implementation of a simple approach for modified the Zener-Hollomon parameter considering the compensation of strain rate and temperature increment. By comparing the predicted and experimented values, the correlation coefficient and mean absolute relative error are 0.997 and 2.363%, respectively. The quantitative statistical results indicate that the proposed constitutive model can precisely characterize the hot deformation behavior of ZHMn34-2-2-1 manganese brass.

Abstract: We study the effects of two scaling exponents on the mechanical properties of swollen elastomers under equibiaxial and planar extensions. Two scaling exponents are introduced to extend the Flory-Rehner free energy function, and are adjusted based on the previous study. Results show that swelling-induced strain softening is apt to occur under equibiaxial extension compared to uniaxial extension. The additional tensile stress in a lateral direction enables it to occur in relatively poor solvents, and accelerates the onset point. Planar extension shows more complicated responses because the stress in the constrained direction changes dramatically depending on the combination of two scaling exponents and the Flory-Huggins interaction parameter.

Abstract: Relaxation oscillation is a nonlinear dynamic phenomenon, commonly observed in viscous-plastic deformation of materials. However, it is the first time that we observed this phenomenon in the viscous flow of borosilicate glass in its super-cooled liquid region. Our investigation identified that the oscillation is caused by the particular microstructure of borosilicate glass. Specifically, the structure of borosilicate glass consists of borate-rich and silicate-rich networks. During the viscous flow, the fast deformation in borate network tends to be localized. However, the network mixing reaction between the borate-rich and silicate-rich networks can slowly relax the fast localized deformation. These two processes occur simultaneously and as a result bring about the relaxation oscillation. Based on this mechanism, the study established a physical constitutive model to predict the relaxation oscillation during the compression of borosilicate glass.

Abstract: The deformation behavior of supermartensitic and martensitic stainless steels was investigated through compression test using Gleeble-3800 thermo-mechanical simulator within the temperature range of 900 – 1200 ^оС and the strain rates range of 0.01 – 10 s^-1. The results showed that the flow stress and the peak strain increase with the drop in the deformation temperature and the rise in the strain rate. Flow stress of SMS steel exceeds flow stress of MS steel for same regimes of deformation. The difference in flow stress increases with the increase in Zener-Hollomon parameter, but does not exceed 15 MPa. The critical deformation, required to start dynamic recrystallization, for supermartensitic stainless steel is slightly lower than for martensitic stainless steel. The hot deformation activation energy of steels is also investigated, their values are similar and equal to 432 and 440 kJ/mol for MS and SMS steel, respectively.

Abstract: Flow behavior and microstructure evolution of 2297 Al-Cu-Li alloy were investigated by isothermal compression tests conducted at the deformation temperature of 300-500°C and strain rates of 0.001-10s-1. The results demonstrate that the characteristics of stress-strain curves depended on the interaction of work hardening and dynamic softening. The true stress increased with the decreasing of temperature and the increasing of the strain rate. At a given deformation condition, the flow curve consisted of three stages: stage I (work hardening stage), stage II (softening stage) and stage III (steady stage). Deformation temperature and strain rate had a great influence on microstructure evolution. 2297 alloy deformed at low temperature (300°C) and high strain rate (10s-1) showed a DRV characteristic. As deformed at high temperature (500°C) and low strain rate (0.001s-1), DRX gradually become the main softening mechanism. The measured flow stress was friction corrected and then employed to develop constitutive equations on the basis of the Arrhenius-type equation by considering the effect of the strain on material constants by a sixth orders polynomials. Flow stress value of 2297 alloy predicted by the proposed constitutive equations shows a good agreement with experimental results, thereby confirming the validity of the developed constitutive relation.

Abstract: The effect of thermal processing (TMP) parameters on grain growth in a low C - Mn steel and a C - Mn steel microalloyed with Nb, Ti and V were compared as part of a wider study on grain growth in microalloyed steels. The grain growth rate was found to be low at low temperatures and short soaking times but increases significantly with both increasing temperature and time. The activation energy Q, the grain growth equation constants n and A were found to be higher in the microalloyed steel than the plain C-Mn steel. A constitutive model for predicting austenite grain growth in the low C-Mn steel and the microalloyed steel has been developed. The predictive potential of the model is in good agreement with the experimental data.

Abstract: The present paper is concerned with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10^-3 to 10³/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves up to strains of nearly 0.08 for four different commercially available extruded polymers were determined on the standard split Hopkinson pressure bar (SHPB). The low and intermediate strain-rate compressive stress-strain relations were measured in an Instron testing machine. Six parameters in the modified Ramberg-Osgood equation were determined by fitting to the experimental stress-strain data using a least-squares fit. It was shown that the monotonic compressive stress-strain behavior over a wide range of strain rates can successfully be described by the modified Ramberg-Osgood constitutive model. The limitations of the model were discussed.

Abstract: We develop a novel constitutive modeling approach for the analysis of fracture propagation in quasi-brittle materials using the Material Point Method. The kinematics of constitutive models is enriched with an additional mode of localized deformation to take into account the strain discontinuity once cracking has occurred. The crack details therefore can be stored at material point level and there is no need to enrich the kinematics of finite elements to capture the localization caused by fracturing processes. This enhancement also removes the drawback of classical smeared crack approach in producing unphysical snapping back constitutive responses when the spatial resolution is not fine enough. All these facilitate the implementation of the new approach in the Material Point Method for analysis of large scale problems. Numerical examples of fracture propagation are used to demonstrate the effectiveness and potentials of the new approach.