• Advances in materials Research
• /
• v.11 no.4
• /
• pp.351-374
• /
• 2022

Softening function is the primary input for modeling the fracture of concrete when the cohesive crack approach is used. In this paper, based on the laboratory data on notched beams, an inverse algorithm is proposed that can accurately find the softening curve of the concrete. This algorithm uses non-linear finite element analysis and the damage-plasticity model. It is based on the kinematics of the beam at the late stages of loading. The softening curve, obtained from the corresponding algorithm, has been compared to other softening curves in the literature. It was observed that in determining the behavior of concrete, the usage of the presented curve made accurate results in predicting the peak loads and the load-deflection curves of the beams with different concrete mixtures. In fact, the proposed algorithm leads to softening curves that can be used for modeling the tensile cracking of concrete precisely. Moreover, the advantage of this algorithm is the low number of iterations for converging to an appropriate answer.

• Transactions of Materials Processing
• /
• v.7 no.3
• /
• pp.274-281
• /
• 1998

The service life of tools in metal forming process is to a large extent limited by wear, fatigue fracture and plastic deformation. In elevated temperature forming processes wear is the predominant factor for tool operating life. To predict tool life by wear Achard's model is generally applied. Usually hardness of die is considered to be a function of temperature. But hardness of die is a function of not only tem-perature but also operating time of die. To consider softening of die by repeated operation it is necessary to express hardness of die by a function of a function of temperature and time. By experiment of reheating of die softening curve was obtained and applied to suggest modified Archard's Model in which hardness is a function of main tempering curve.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1998.03a
• /
• pp.88-93
• /
• 1998

The service life of tools in metal forming process is to a large extent limited by wear, fatigue fracture and plastic deformation. In warm forging processes wear is the predominant factor for operating lives of tools. To predict tool life by wear, Archard's wear model is generally applied. Usually hardness of die is considered to be a function of temperature in Archard's wear model. But hardness of die is a function of not only temperature but also operating time of die. To consider softening of die by repeated operations, it is necessary to express hardness of dies by a function of temperatures and operating time. By experiment of reheating of dies, die softening curves were obtained. Finally modified Archard's wear model in which hardness of die was expressed as a function of main tempering curve was proposed.

• Geomechanics and Engineering
• /
• v.7 no.4
• /
• pp.335-353
• /
• 2014

The softening hyperelastic model based on the strain energy limitation is of clear concepts and simple forms to describe the failure of materials. In this study, a linear and a nonlinear softening hyperelastic model are proposed to characterize the deformation and the failure in granular materials by introducing a softening function into the shear part of the strain energy. A method to determine material parameters introduced in the models is suggested. Based on the proposed models the numerical examples focus on bearing capacity and strain localization of granular materials. Compared with Volokh softening hyperelasticity and classical Mohr-Coulomb plasticity, our proposed models are able to capture the typical characters of granular materials such as the strain softening and the critical state. In addition, the issue of mesh dependency of the proposed models is investigated.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2008.10a
• /
• pp.304-307
• /
• 2008

In order to evaluate the effect of permanent softening behavior on springback prediction, 2D-draw bending simulations were compared with experiments for friction stir welded DP590 steel sheets. To account fur the nonlinear hardening behavior, the combined isotropic-kinematic hardening law was utilized with and without considering the permanent softening behavior during reverse loading. Also, the non-quadratic orthotropic yield function, Yld2000-2d, was used to describe the anisotropic initial-yielding behavior of the base sheet while anisotropic properties of the weld zone were ignored for simplicity.

• Transactions of Materials Processing
• /
• v.18 no.4
• /
• pp.329-335
• /
• 2009

In order to better predict the springback for friction stir welded DP590 steel sheet, the combined isotropic-kinematic hardening was formulated with considering the permanent softening behavior during reverse loading. As for yield function, the non-quadratic anisotropic yield function, Yld2000-2d, was used under plane stress condition. For the verification purposes, comparisons of simulation and experiments were performed here for the unconstrained cylindrical bending, the 2-D draw bending tests. For two applications, simulations showed good agreements with experiments.

• Structural Engineering and Mechanics
• /
• v.32 no.3
• /
• pp.459-475
• /
• 2009

This paper presents analytical methodologies for remaining life prediction of plain concrete structural components considering tension softening and size effects. Non-linear fracture mechanics principles (NLFM) have been used for crack growth analysis and remaining life prediction. Various tension softening models such as linear, bi-linear, tri-linear, exponential and power curve have been presented with appropriate expressions. Size effect has been accounted for by modifying the Paris law, leading to a size adjusted Paris law, which gives crack length increment per cycle as a power function of the amplitude of a size adjusted stress intensity factor (SIF). Details of tension softening effects and size effect in the computation of SIF and remaining life prediction have been presented. Numerical studies have been conducted on three point bending concrete beams under constant amplitude loading. The predicted remaining life values with the combination of tension softening & size effects are in close agreement with the corresponding experimental values available in the literature for all the tension softening models.

• Computers and Concrete
• /
• v.1 no.4
• /
• pp.433-455
• /
• 2004

The paper presents results of FE-calculations on shear localizations in quasi-brittle materials during both an uniaxial plane strain compression and uniaxial plane strain extension. An elasto-plastic model with a linear Drucker-Prager type criterion using isotropic hardening and softening and non-associated flow rule was used. A non-local extension was applied in a softening regime to capture realistically shear localization and to obtain a well-posed boundary value problem. A characteristic length was incorporated via a weighting function. Attention was focused on the effect of mesh size, mesh alignment, non-local parameter and imperfections on the thickness and inclination of shear localization. Different methods to calculate plastic strain rates were carefully discussed.

• Elastomers and Composites
• /
• v.42 no.3
• /
• pp.168-176
• /
• 2007

When the rubber vulcanizates reinforced with carbon black or silica are subjected to cyclic loading from its virgin state, the stress required on reloading is less than that on the initial loading. This stress softening phenomenon is referred to as the Mullins effect. The strain energy function of rubber vulcanizates was investigated using theory of pseudo-elasticity incorporated damage parameter that Ogden and Roxburgh have proposed to describe the damage-induced stress softening effect in rubber-like solids. The quasi-static cyclic loading test was performed using the NR-SBR vulcanizates reinforced with carbon black, and then the effect of a damage parameter to stress-strain curve in reloading and subsequent reloading paths was studied. The strain energy function of the rubber vulcanizates with a different filler content was also evaluated.

• Geomechanics and Engineering
• /
• v.18 no.3
• /
• pp.225-234
• /
• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.