Modeling the Interaction between Vacancies and Grain Boundaries during Ductile Fracture

The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenomenon remains not fully understood.This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects.This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy.Subsequently,a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries.This model is first verified and validated through comparison with some available analytical solutions,demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy.A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation.The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries,potentially facilitating void nucleation in ductile fracture.

Effect of Sulfur Content and Sulfide Shape on Fracture Ductility in Case Hardening Steel

The effects of sulfur content and calcium addition on smooth axisymmetric tensile fracture ductility of case hardening steel DIN 18CrNiMo7-6 have been investigated. The quantitative metallographic analysis of sulfide inclusions and the correlations between sulfide inclusions and fracture ductility were examined. Sulfide inclusions were found to have deleterious effect on fracture ductility, whereas the effect can be offset to some extent by calcium-treat- ment due to less easily deforming of sulfides during hot-working. The product （AA·λAW） of sulfide inclusion area fraction （An） and its area-weighted aspect ratio （λAW） can be used as a parameter to describe the effect of sulfide inclusions on fracture true strain.

Evaluation of varying ductile fracture criterion for 7075 aluminum alloy

As one of the principal failures,ductile fracturing restricts metal forming process.Cockcroft-Latham type fracture criterion is suited for ductile fracture in bulk metal-forming simulation.Finding a way to evaluate the ductile fracture criterion（DFC） and identify the relationship between DFC and deformation conditions for a strain-softening material,7075 aluminum alloy;however,it is a non-trivial issue that still needs to be addressed in a greater depth.An innovative approach is brought forth that the compression tests and numerical simulations provide mutual support to evaluate the ductile damage cumulating process and determine the DFC diagram.One of the results shows that for a fixed temperature,the maximum cumulated damage decreases regularly with increasing strain rate.The most important result shows that DFC of 7075 aluminum alloy at temperatures of 573-723 K and strain rates of 0.01-10 s-1 is not a constant but a change in a range of 0.255-0.453,thus it has been defined with varying ductile fracture criterion（VDFC） and characterized by a function of strain rate and temperature.According to VDFC diagram,the exact fracture moment and position during various forming processes will be predicted conveniently,in addition to which,the deformation domains with lower fracture risk corresponding to higher VDFC can be identified.

Modified MK model combined with ductile fracture criterion and its application in warm hydroforming

A modified MK model combined with ductile fracture criterion（DFC-MK model） is proposed to compute the forming limit diagrams（FLDs） of 5A06-O aluminum alloy sheet at different temperatures.The material constant（C） of ductile fracture criterion and initial thickness imperfection parameter（f0） at various temperatures are determined by using a new computing method based on wide sheet bending test.The FLDs at 20 and 200 °C are calculated through the DFC-MK model.The DFC-MK model,which includes the influence of through-thickness normal stress,is written into the subroutine VUMAT embedded in Abaqus/ Explicit.The cylindrical cup hydroforming tests are carried out to verify the model.The results show that compared with experimental observations,the predicted FLDs based on DFC-MK model are more accurate than the conventional MK model;the errors between the simulations and experiments in warm hydroforming are 8.23% at 20 °C and 9.24% at 200 °C,which verify the effectiveness of the proposed model.

Comparison of Modified Mohr-Coulomb Model and Bai-Wierzbicki Model for Constructing 3D Ductile Fracture Envelope of AA6063

Ductile fracture of metal often occurs in the plastic forming process of parts.The establishment of ductile fracture criterion can effectively guide the selection of process parameters and avoid ductile fracture of parts during machining.The 3D ductile fracture envelope of AA6063-T6 was developed to predict and prevent its fracture.Smooth round bar tension tests were performed to characterize the flow stress,and a series of experiments were conducted to characterize the ductile fracture firstly,such as notched round bar tension tests,compression tests and torsion tests.These tests cover a wide range of stress triaxiality(ST)and Lode parameter(LP)to calibrate the ductile fracture criterion.Plasticity modeling was performed,and the predicted results were compared with corresponding experimental data to verify the plasticity model after these experiments.Then the relationship between ductile fracture strain and ST with LP was constructed using the modified Mohr-Coulomb(MMC)model and Bai-Wierzbicki(BW)model to develop the 3D ductile fracture envelope.Finally,two ductile damage models were proposed based on the 3D fracture envelope of AA6063.Through the comparison of the two models,it was found that BW model had better fitting effect,and the sum of squares of residual error of BW model was 0.9901.The two models had relatively large errors in predicting the fracture strain of SRB tensile test and torsion test,but both of the predicting error of both two models were within the acceptable range of 15%.In the process of finite element simulation,the evolution process of ductile fracture can be well simulated by the two models.However,BW model can predict the location of fracture more accurately than MMC model.

Effect of solution treatment time on plasticity and ductile fracture of 7075 aluminum alloy sheet in hot stamping process

The effect of solution treatment time on the post-formed plasticity and ductile fracture of 7075 aluminum alloy in the hot stamping process was studied.Tensile tests were conducted on the specimens subjected to the hot stamping process with different solution treatment time.The digital image correlation(DIC)analysis was used to obtain the strain of the specimen.Based on the experiments and modeling,the Yld2000-3d yield criterion and the DF2014 ductile fracture criterion were calibrated and used to characterize the anisotropy and fracture behavior of the metal,respectively.Furthermore,the microstructure of specimens was studied.The experimental and simulation results indicate that the 7075 aluminum alloy retains distinct anisotropy after the hot stamping process,and there is no obvious effect of extending the solution treatment time on the material anisotropy.However,it is found that a longer solution treatment time can increase the fracture strain of the aluminum alloy during the hot stamping process,which may be related to the decrease of the second-phase particles size.

A NEW DUCTILE FRACTURE THEORY AND ITS APPLICATIONS

This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characteriz;e various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility Of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness values J(1c) and delta(c) with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameters J(dc) and delta(dc) are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.

Fracture Characterization of High-Density Polyethylene Materials Using the Energetic Criterias

Impact behavior of polymers has received considerable attention in recent years,and much work based on fracture mechanic approaches has been carried out.In this paper,fracture behavior in large deformation of a high density polyethylene(HDPE)materials was investigated through experimental impact testing on single edge notched specimen(SENB)and by using theoretical and analytical fracture criteria concepts.Moreover,a review of the main fracture criteria is given in order to characterize the toughness of this polymer in the both cases(static and dynamic).The fractured specimens obtained from the Charpy impact test were characterized with respect to their fracture surfaces.Characteristic zones of the fracture surface can be assigned to different stages and mechanisms of the fracture process.Finally,for a better understanding of fracture and damage mechanisms and to provide the best estimation of fracture toughness in impact,an experimental approach based on microscopic observations(SEM)was used.

Ductile fracture behavior of TA15 titanium alloy at elevated temperatures

To better understand the fracture behavior of TA15 titanium alloy during hot forming, three groups of experiments were conducted to investigate the influence of deformation temperature, strain rate, initial microstructure, and stress triaxiality on the fracture behavior of TA15 titanium alloy. The microstructure and fracture surface of the alloy were observed by scanning electronic microscopy to analyze the potential fracture mechanisms under the experimental deformation conditions. The experimental results indicate that the fracture strain increases with increasing deformation temperature, decreasing strain rate, and decreasing stress triaxiality. Fracture is mainly caused by the nucleation, growth, and coalescence of microvoids because of the breakdown of compatibility requirements at the α/β interface. In the equiaxed microstructure, the fracture strain decreases with decreasing volume fraction of the primary α-phase(αp) and increasing α/β-interface length. In the bimodal microstructure, the fracture strain is mainly affected by α-lamella width.

Study on fracture behavior of SiCp/A356 composites

The fracture behavior of SiCp/A356 composite at room and high temperatures was studied. Under tensile stress condition at room temperature, the fracture is mostly a combination of the brittle fracture of SiC particles and ductile fracture of A356 matrix. As the tensile temperature increases, the composite changes the main fracture behavior to the separation fracture of the bonding surface between SiC particles and A356 matrix. When the tensile temperature reaches 573 K, the fracture behavior of the composites is almost the whole separation fracture of the bonding surface, which is the main strengthening mechanism at high temperature. Under the cycle stress condition at room and high temperatures, the main fracture behavior of the composites is always a combination of the brittle fracture of SiC particles and ductile fracture of A356 matrix. However, under the cycle stress at high temperature, cycle behavior of the composites changes from cycle hardening at room temperature to the cycle softening at high temperature.

PREVENTION OF THE INTERGRANULAR FRACTURE AT ELEVATED TEMPERATURES BY ADDITION OF PHOSPHORUS TO A HIGH PURITY Fe0 002% SALLOY

Theeffectof phosphorusonthehotductility andthesegregation ofsulfuratgrain boundariesin high purityironcontaining 0 002 % sulfur werequantitativelyinvestigated bytensiletestat973 K, SEMobservation of fracture surface and scanning Auger electron spectroscopy.Theexperimental resultscan besum marized as follows:(1) addition of phosphorustothe iron remarkablysuppressestheintergranular fractureinduced bythesegregation of sulfur at973 Kandincreasesthe hot ductility;(2) phosphorusstrikingly decreasesthesegregation ofsulfur atgrain boundaries, whichisresponsibleforthesuppressionoftheintergranularfrac tureat973 K;(3) theremarkably decreasedsegregation ofsulfur atgrain boundariesbytheaddition of phosphoruscan beexplained bythesitecompetitioneffectandtherepulsiveinter action at grain boundariesbetweensulfuratomsand phosphorusatoms;(4) sulfurstrikinglysegregatestothevoid surfacesformed on grain boundaries, while phosphorushaslittlesegre gationtothevoid surfaces.

DIMPLE FORMATION ON FRACTURE SURFACE OF STEEL 55SiMnMo

The fracture surface of the normalized steel 55SiMnMo was observed,under tensile device at- tached on the SEM,to be of ductile dimple feature on the bainite which is composed of lath ferrite and austenite platelet.The dimple is essentially nucleated in the ferrite.Because the austenitic plastic deformation is remarkable during fracturing,the tear ridge of dimple is very sharp.

Fracture toughness of 12Cr2Mo1R steel at elevated temperature

The microstructure, tensile properties, and fracture toughness of 12Cr2Mo1R steel were studied. The results indicate that this steel is characterized by a bainite microstructure, in which several types of carbides precipitate along the ferrite laths. As the temperature increases from room temperature to 375℃ ,the strength of the steel increases slightly and the fracture toughness clearly decreases. However, when the temperature continues to increase up to 500 ℃, the strength decreases and the fracture toughness increases. At all the temperatures investigated,the strength and toughness of the developed 12Cr2Mo1R steel were capable of meeting the design requirements of a high-temperature gas-cooled reactor. The fracture of 12Cr2Mo1R steel at high temperature typically occurs in the ductile mode.

Energy consumption for creep fracture of metallic materials

The energy conservation law is applied to formulate the ductile and brittle creep fracture criterion for metallic materials. The criterion contains a summary of heat and latent energies. Assuming that the heat energy is given out so it has no effect on the fracture process, the ductile creep fracture criterion is simplified. To take into account the evaluation of the damage state of materials the compressibility condition is introduced and the brittle creep fracture law is formulated.

Experimental Evaluation of Ductile Fracture of Sheet Metals under Plane Stress States

With the application of lightweight materials such as advanced high-strength steel and aluminum alloy in the automotive industry, it is necessary to quantitatively evaluate the ultimate deformation capacity of materials under various plane stress states for the digital simulation of these materials. Conventional Nakajima test can only provide three regular plane stress states, such as tension, plane strain tension and bulging, and FLC curve is affected by deformation path, mold lubrication and other variables. More importantly, Nakajima test cannot provide shear, tension shear, which are extremely important loading conditions in automobile collisions. Therefore, the research work of this paper focuses on the evaluation of the ultimate ductile fracture behavior of sheet metals under various conditions of plane stress states. The four variables Mohr-Coulomb model was established to study the ductile fracture of metal sheets under plane stress states. Beginning with the recorded minor and major strain distributing on the deformation area of uniaxial tension samples, Moving Regression Algorithm was deployed to reveal the inherent relationship among the key parameters involved in the M-C model, which also provided an experimental technique for monitoring the instantaneous changing of triaxiality over the whole loading period. Three or four typical types of uniaxial-loading specimens were well designed to determine the M-C curve. As a result, M-C curve and the transformed major stain vs. minor strain curve provide further information about the material arrest to the ductile fracture in the area of shear loading, in comparison with the conventional FLD test.

Numerical simulation and optimization of process parameters in fineblanking process

Fineblanking process is a typical large localized plastic deformation process. Based on its forming characteristics, a numerical model is established and an elasto-plastic simulation is performed using the finite element method （FEM）. The re-meshing method is used when the severe element distortion occurs to facilitate further computation and avoid divergence. The McClintock fracture criterion is adopted to predict and determine the time and site of crack initiation and propagation. Based on this numerical model, the distribution and developing trend of the stress and strain in the shearing zone are predicted. Furthermore, the influence of several process parameters, such as punch-die clearance, edge radius of punch and die, V-ring force, counter force, etc., on the blanked quality is analyzed. The discipline is in accordance with the actual manufacture situation, which can be a guidance to optimization of process parameters.

Dynamic Phase Field Description on Ductile Fracture Process

In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.

Limestone mechanical deformation behavior and failure mechanisms： a review

In this paper, several mechanical deformation curves of limestone are reviewed, and the effects of temperature, confining pressure, and fluid are discussed. Generally, Mohr–Coulomb is used for limestone brittle fracture. The characteristic of low temperature cataclastic flow and the conditions and constitutive equations of intracrystal plastic deformation such as dislocation creep,diffusion creep, and superplastic flow are discussed in detail. Specifically, from the macroscopic and microscopic view, inelastic compression deformation(shear-enhanced compaction) of large porosity limestone is elaborated.Compared with other mechanics models and strength equations, the dual porosity(macroporosity and microporosity) model is superior and more consistent with experimental data. Previous research has suffered from a shortage of high temperature and high pressure limestone research; we propose several suggestions to avoid this problem in the future:(1) fluid-rock interaction research;(2) mutual transition between natural conditions and laboratory research;(3) the uniform strength criterion forshear-enhanced compaction deformation;(4) test equipment; and(5) superplastic flow mechanism research.

Comparative study on forming limit prediction of AA7075-T6 sheet with M−K model and Lou−Huh criterion

In order to effectively predict the fracture of AA7075-T6 sheet, the forming limit curves of AA7075-T6 high-strength sheet were drawn according to Morciniak Kuczyski (M K) model and Lou Huh criterion, respectively. The errors between the predicted values of the two theoretical prediction models and experimental values were calculated by error analysis. The forming limit curves were verified by the punch stretch test to evaluate the prediction accuracy of M K model and Lou Huh criterion. The error analysis results show that the mean error of Lou Huh criterion with the optimal parameters for all tensile specimens is 25.04%, while the mean error of M K model for all tensile specimens is 74.24%. The prediction accuracy of Lou Huh criterion in predicting the fracture of AA7075-T6 sheet is higher. The punch stretch test results show that the forming limit curve drawn by Lou Huh criterion can effectively predict the fracture of AA7075-T6 sheet, but the prediction accuracy of M K model is relatively poor.

Damage evolution model of strain hardening cementitious composites under the uniaxial stress state

The deformation and damage behaviors of strain hardening cementitious composites （SHCC） under the uniaxial stress state were investigated in this paper. Two ductile failure-based constitutive models were introduced to describe the uniaxial tension and compression properties of SHCC only using a few parameters. The computation method of model parameters was developed to ease the simulation procedures. Damage evolution of the SHCC was simulated by the formulation of continuum damage mechanics subsequently. The results show that the proposed models fit the stress-strain curves reasonably well, and the damage variables show different growth rules under uniaxial tension and compression. It is concluded that the proposed method can not only simply simulate the constitutive behavior of SHCC with the reasonable accuracy but also capture the characteristic of material degradation.