A Study of Large Plastic Deformations in Dual Phase Steel Using Digital Image Correlation and FE Analysis

Large plastic deformation in sheets made of dual phase steel DP800 is studied experimentally and numerically. Shear testing is applied to obtain large plastic strains in sheet metals without strain localisation. In the experiments, full-field displacement measurements are carried out by means of digital image correlation, and based on these measurements the strain field of the deformed specimen is calculated. In the numerical analyses, an elastoplastic constitutive model with isotropic hardening and the Cockcroft–Latham fracture criterion is adopted to predict the observed behaviour. The strain hardening parameters are obtained from a standard uniaxial tensile test for small and moderate strains, while the shear test is used to determine the strain hardening for large strains and to calibrate the fracture criterion. Finite Element (FE) calculations with shell and brick elements are performed using the non-linear FE code LS–DYNA. The local strains in the shear zone and the nominal shear stress-elongation characteristics obtained by experiments and FE simulations are compared, and, in general, good agreement is obtained. It is demonstrated how the strain hardening at large strains and the Cockcroft–Latham fracture criterion can be calibrated from the in-plane shear test with the aid of non-linear FE analyses. An erratum to this article can be found at     

On the temperature dependence of fracture toughness in the brittle-to-ductile transition region

A method for calculation of fracture toughness in the brittle-to-ductile transition region is proposed for a known fracture toughness at a given temperature and a known temperature dependence of the yield point. A two-parameter quasi-brittle fracture criterion proposed earlier is employed. This criterion contains in explicit form a plastic constraint factor that is sensitive to temperature variation under plane strain conditions. The obtained calculation dependence is compared with experimental data for four structural steels. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 80–86, April, 1999.     

On constructing the theory of ductile fracture near friction surfaces

A criterion of ductile fracture is proposed, which takes into account the singular character of theoretical solutions near the maximum friction surfaces and the emergence of a thin layer with intense plastic strains near surfaces with high friction stresses in real processes of metal forming. The equation for the thickness of the layer with intense plastic strains and the fracture criterion include the strain rate intensity factor, apparently, characterizing the intensity of physical processes that occur in a thin material layer near the friction surfaces. Some experimental data are used to determine the thickness of this layer. The ductile fracture criterion is analyzed by solving the problem of strip extrusion under conditions of plane strain deformation.     

Generation of cracks in a perforated reinforced plate

A problem of fracture mechanics on crack nucleation in a reinforced plate attenuated by a periodic system of circular holes is considered. Crack nucleation is modeled by a pre-fracture band in the plastic flow state with a constant stress, which is considered as a region of attenuated bonds between material particles. Determining unknown parameters characterizing the emerging crack reduces to solving a singular integral equation. The condition of crack emergence is formulated with allowance for the criterion of the limiting opening of the faces of the material pre-fracture band. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 170–180, November–December, 2008.     

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G _max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ _y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Localized deformation and fracture of polycrystals at mesolevel

Recent experiments have shown that shear band formation and rotation of structural elements at the mesolevel are fundamental to the development of plastic deformation and fracture of solids. Attention should be focused on a mesovolume of deformed material because the local stress and strain differ from those averaged at the macroscale. The discrete nature of the microshears and restricted deformation of the mesofragments should be accounted for. Rotation of the different mesofragments being parts of a grain, grains, grain conglomerates, etc., plays an important role in plasticity. Moreover, knowledge of the local parameters is needed for developing plasticity theories and fracture criteria. Models have been proposed within the framework of the physical mesomechanics. They take into account structural elements of different scales for simulating shear band nucleation and propagation in addition to mesofragment rotations. Calculations have been made for different mesovolumes under dynamic loading. In this work, a new criterion of plasticity is considered at the mesolevel. It accounts for the nucleation of plastic shears at the surfaces and interaction of structural elements. The numerical technique combines both the continuum mechanics approach and discrete cellular automata method.     

A mesomechanical fracture model for an orthotropic material with different tensile and compressive strengths

The paper addresses a fracture problem for an orthotropic cracked plate made of a material with different tensile and compressive strengths and subjected to biaxial loading. The problem is solved using a micromechanical fracture model proposed earlier by the authors. It is assumed that the fracture of the material in the fracture process zones at the crack front is described by the Gol’denblat–Kopnov failure criterion. Strength curves for an orthotropic cracked plate with different strength and fracture-toughness parameters are plotted     

Limiting state of an elastoplastic orthotropic plate with a periodic system of collinear cracks

A modified Dugdale model is used to study the fracture of an orthotropic elastoplastic plate with a periodic system of rectilinear cracks. The material of the plate obeys a general yield criterion. The general form of solution is obtained in terms of Kolosov-Muskhelishvili potentials. The size of the plastic zone is expressed in terms of the external load and geometrical parameters. The equations for the determination of the stresses in the plastic zone and the crack opening displacement are derived. The effect of anisotropy on the formation of the plastic zones at the crack tip is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 80–88, May 2007.     

Stress state in the plastic zone on the continuation of an elliptic mode I crack under bi-and tri-axial loading

The spatial stress state in a circular plastic zone near an elliptic crack under bi-and tri-axial asymmetric loading at infinity is studied. It is shown that the plastic constraint factor peaks at the points with maximum external tensile tangential stresses on the crack boundary. The use of a two-parameter failure criterion leads to the conclusion that the limit state can first be reached at the ends of the major axis of the elliptic crack depending on the relation between the external stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 24–30, November 2007.     

Qualitative Distinctions in the Solutions Based on the Plasticity Theories with the Mohr-Coulomb Yield Criterion

The following two models of the plasticity theory are considered: the model with the Mohr-Coulomb yield criterion and the classical model of the plasticity theory with a yield criterion independent of the mean stress. The deformation problem of a plastic layer enclosed between two rotating plates is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 136–145, November–December, 2005.     

Optimization formulation of the evolutionary problem of crack propagation under quasibrittle fracture

For the evolutionary problem describing crack propagation in a solid with allowance for the irreversible work of plastic deformation due to the crack propagation, a general optimization formulation is proposed and investigated. For the optimum crack, data on the H²-smoothnesses of the displacement field in the solid and, hence, on the finiteness of the stress at the crack tip, are obtained. The solvability of the optimization problem (i.e., the existence of an optimum crack) is proved for a curvilinear crack propagation path specified a priori. For the particular case of a straight path, a generalized criterion of crack growth is proposed. The question of the choice of a crack propagation path is discussed and a comparison with existing fracture criteria is made. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 107–118, September–October, 2006.     

Structural approach in problems of the limit equilibrium of brittle solids with stress concentrators

Versions of the formulation of a two-dimensional fracture criterion are discussed. Possible methods for determining the value of the structural fracture parameter are analyzed. Theoretical estimates are compared with experimental data and results obtained using alternative criteria. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 162–172, July–August, 2007.     

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

The generalized Dugdale crack model is used to formulate two-parameter failure criteria for the cases of quasibrittle state and developed plastic zones at a mode I crack tip. The failure criteria relate the fracture strength characteristics and the stress mode at the crack tip through the plastic constraint factor. The critical state of bodies with cracks under uni-and biaxial loading is analyzed in the cases of plane stress and plane strain using the Tresca and von Mises yield criteria. A small-scale yield criterion, which is an analytic relation between the critical stress intensity factor and T-stresses, is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 47–57, July 2007.     

Aging in the cortical bone: a constitutive law and its application

It is well known that the material behavior of human cortical bone changes from ductile to more brittle due to aging. This process is accompanied by a decrease of the maximum specific deformation energy. Numerous mechanical tests of specimens have shown a relationship between the mechanical behavior, age and microstructure, especially the porosity, mineralization and fraction of the secondary osteonal area. But up to now, this relationship is not explicitly considered in a constitutive law. Measured stress–strain curves, taken from the literature, from one-dimensional mechanical experiments in tension (McCalden et al. in J Bone Joint Surg Am 75(8):1193–1205, 1993) have been characterized by Young’s modulus, elastic, plastic and fracture energy, fracture stress and strain. The specimens have been harvested from the femora of 46 deceased individuals. Based on this data, we set up a system of equations taking into account the microstructure of the bone material by analogy to common procedures in fracture and damage mechanics. Solving this system for all measured experimental data leads to the determination of the independent damage parameters for each individual person. It turned out that some characteristic mechanical values and one independent damage parameter are statistically significant dependent on age and microstructure. We receive a constitutive law, which describes the mechanical behavior up to fracture by measurable parameters for the microstructure and the individual age and gender only. In turn, we calculate the individual tolerable load for bending, using a nonlinear stress–strain curve, and postulate an age-dependent fracture load for healthy bone by means of the statistical regression. Deviation from the standard is an indication for a bone disease in particular for osteoporosis.     

Plastic Bending of a Strip for a Yield Criterion Depending on the Mean Stress

The plane-strain plastic bending of a wide strip is considered under the assumption that the material of the strip obeys the Coulomb-Mohr yield criterion and the two types of kinematic relations proposed by Spencer and Hill. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 120–125, March–April, 2006.     

One plasticity model for problems of plastic metal working

Scalar and tensor models of plastic flow of metals extending plasticity theory are considered over a wide range of temperatures and strain rates. Equations are derived using the physico-phenomenological approach based on modern concepts and methods of the physics and mechanics of plastic deformation. For hardening and viscoplastic solids, a new mathematical formulation of the boundary-value plasticity problem taking into account loading history is obtained. Results of testing of the model are given. A numerical finite-element algorithm for the solution of applied problems is described. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 159–169, November–December, 2008.     

Types of Localization of Plastic Deformation and Stages of Loading Diagrams of Metallic Materials with Different Crystalline Structures

Macrolocalization, which accompanies the process of plastic deformation beginning from the yield point and ending by fracture, is determined by the staged character of material-loading diagrams. The evolution of localization patterns in a plastic flow of body-centered cubic vanadium alloy, hexagonal close-packed magnesium alloy, tetragonal tin, and face-centered cubic submicrocrystalline aluminum is analyzed within this concept. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 176–184, March–April, 2006.     

The surface-forming energy release rate based fracture criterion for elastic–plastic crack propagation

The J-integral based criterion is widely used in elastic–plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic–plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR. From the most concise formula, it is interesting to note that the surface-forming ERR can be computed using only the stress and deformation of the current moment, and the definition of the energy density or work density is avoided. When an infinitesimal contour is chosen, the expression can be further simplified. For any fracture behaviors, the surface-forming ERR is proven to be path-independent, and the path-independence of its constituent term, so-called J_s-integral, is also investigated. The physical meanings and applicability of the proposed surface-forming ERR, traditional ERR, J_s-integral and J-integral are compared and discussed. Besides, we give an interpretation of Rice paradox by comparing the cohesive fracture model and the surface-forming ERR based fracture criterion.     

Evaluating rock mass failure in the vicinity of slot cuts

A comparative analysis of the failure of rock with surfaces of weakness in the vicinity of elongated clot cuts of rectangular cross section was performed using the boundary integral equation method and the Mohr-Kuznetsov strength criterion. The rock failure coefficient was used as the criterion of breaking. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 129–133, January–February, 2008.