Simulation of chevron crack formation and evolution in drawing

The objective of the present work is to clarify ductile fracture phenomena in bulk metal forming, by means of finite-element analyses and experiments. We have developed a computer program, based on a conventional computer program of the finite-element method, by which the behavior of crack propagation after ductile fracture can be analyzed. The phenomenon that inner fracture defects occur periodically in the axial direction in drawing has been simulated using the computer program. The following results were obtained. First, to analyze multipass drawing we have proposed a method of calculating residual stress after drawing and a method of considering initial stress before drawing. Second, to perform accurate simulation, we have developed a method of fracturing one element in each step and a method of separating nodes at the fracture. Finally, we have proposed a method for evaluating ductile fracture in terms of void volume fraction and axial stress, and we have shown the validity of the method by comparing the analytical results with experimental ones.     

Fracture prediction of thin plates under hemi-spherical punch with calibration and experimental verification

The response of thin clamped plates subjected to static punch indentation is investigated experimentally, analytically and numerically to determine the onset of fracture. The accumulated equivalent plastic strain with stress triaxiality as a weighing function is introduced as ductile fracture criterion in the finite-element simulation and analytical prediction. The fracture criterion was calibrated by finite-element simulations of uniaxial tensile tests. Based on the calibration, and calculated distributions and histories of stress and strain, the critical location, and penetration to fracture were predicted within 5–10% accuracy for three punch radii.The plots of force–penetration and locations of fracture initiation in the static punch indentation tests were compared with finite-element simulations and analytical approximations showing good agreement. The transverse deflection profiles of the plates at the point of fracture obtained numerically were shown to agree well with the closed-form solution derived by taking into account a variable stress ratio and varying stress triaxiality. The strain distribution along the plate radius is influenced by the friction between the interfaces of punch and plate. By changing the friction coefficient, the fracture-forming limit diagram was constructed numerically. The present procedure can replace the time-consuming experimental technique in which the strain path is controlled by changing the radius of a cut off.     

A study on chevron crack formation and evolution in a cold extrusion

A numerical algorithm based on the element deletion method and rigid-viscoplastic finite element approach depending on Cockcroft-Latham and specific plastic work fracture criteria was applied to predict formation and evolution of possible cracking in a cold extrusion of aluminum and steel alloys. The Cockcroft-Latham fracture criterion induced an internal crack while an external crack occurred owing to the specific plastic work criterion in simulations. As a result, the Cockcroft-Latham criterion was found to be valid for predicting chevron cracking in comparison with the experimental observation available in the literature. Using the Cockcroft-Latham criterion, cracking was carefully investigated in terms of the size of the crack and gap distance between cracks depending on the number of elements and boundary condition at the punch interface. The critical damage values for the Cockcroft-Latham fracture criterion were also calculated based on the tensile instability and fracture conditions to investigate their effect on possible cracking. Finally, a processing map based on the Cockcroft-Latham fracture criterion for preventing chevron cracking in the cold extrusion of commercially available steel alloy was developed by considering processing parameters such as reduction in area and semicone angle. According to this investigation, the developed element deletion method with the Cockcroft-Latham fracture criterion was reasonably accurate for carrying out chevron cracking analyses in the cold extrusion with proper selection of a critical damage value.     

Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions

An analytical approach for crack identification procedure in uniform beams with an open edge crack, based on bending vibration measurements, is developed in this research. The cracked beam is modeled as two segments connected by a rotational mass-less linear elastic spring with sectional flexibility, and each segment of the continuous beam is assumed to obey Timoshenko beam theory. The method is based on the assumption that the equivalent spring stiffness does not depend on the frequency of vibration, and may be obtained from fracture mechanics. Six various boundary conditions (i.e., simply supported, simple–clamped, clamped–clamped, simple–free shear, clamped–free shear, and cantilever beam) are considered in this research. Considering appropriate compatibility requirements at the cracked section and the corresponding boundary conditions, closed-form expressions for the characteristic equation of each of the six cracked beams are reached. The results provide simple expressions for the characteristic equations, which are functions of circular natural frequencies, crack location, and crack depth. Methods for solving forward solutions (i.e., determination of natural frequencies of beams knowing the crack parameters) are discussed and verified through a large number of finite-element analyses. By knowing the natural frequencies in bending vibrations, it is possible to study the inverse problem in which the crack location and the sectional flexibility may be determined using the characteristic equation. The crack depth is then computed using the relationship between the sectional flexibility and the crack depth. The proposed analytical method is also validated using numerical studies on cracked beam examples with different boundary conditions. There is quite encouraging agreement between the results of the present study and those numerically obtained by the finite-element method.     

Analysis of draw–redraw processes

An analytical model is developed to analyze the draw–redraw processes. Thickening of the flange is modeled using a complete pure radial drawing analysis which takes into account interfacial friction and radial thickness variation. A plastic bending analysis is used to calculate thinning in all forming radii. Material properties, tooling geometry, and process parameters are included in the model. The derivation is then developed into computer subroutines. By arranging the subroutines into the deforming sequence, draw–redraw process can be simulated. The predicted wall thickness profiles agree very well with the experimental measurements. Characterization of wall thickness profile is also discussed.     

镁合金板材温热成形韧性破裂准则

针对镁合金板材温热成形数值模拟过程中无法精确判断材料损伤破裂失稳的技术难题,建立考虑温度效应的镁合金板材温热成形韧性破裂准则;基于单向拉伸试验和温热成形极限试验,采用试验和数值模拟相结合的研究方法,确定镁合金板材温热成形韧性破裂准则中的材料参数;以建立的考虑温度效应的镁合金板材韧性破裂准则作为判断破裂的标准,对AZ31镁合金板材的温热成形极限进行预测,并且通过温热拉延试验进行试验验证。研究结果表明,考虑温度效应的镁合金板材韧性破裂准则适合镁合金温热成形数值模拟,应用建立的韧性破裂准则成功的预测板材温热破裂方式,揭示板材温热成形韧性破裂机理,预测结果与试验结果体现较好的一致性。     

Prediction of Deformed Configuration and Ductile Fracture for Simple Upsetting Using an Artificial Neural Network

This paper suggests a scheme for simultaneously accomplishing the prediction of fracture initiation and geometrical configuration of deformation in metal forming processes using an artificial neural network. A three-layer neural network is used and a back-propagation algorithm is adapted to train the network. The Cockcroft–Latham criterion is used to estimate whether fracture occurs during the deformation process. The geometrical configuration and the value of ductile fracture are measured by the finite-element method. The predictions of the neural network and the numerical results of simple upsetting are compared. The proposed scheme has predicted the geometrical configuration and fracture initiation successfully.     

Ductile fracture and lifetime prediction of structural materials and components under high-temperature creep conditions

The problem of long-term strength prediction of structural materials under uniaxial and biaxial creep conditions, which give rise to ductile fracture, is considered. A new approach to long-term fracture modelling based on constitutive equations of the “isochronous creep theory” and criteria of ductile fracture is suggested. The change in the momentary tangential modulus specifies the materials rheological behaviour and a value tending to zero is assumed as the ductile fracture criterion. Using the model the times to fracture of rods, beams and thin-walled tubes made of high-temperature and heat-resistant materials are estimated and they show good agreement with experimental data.     

Fracture analysis on flexible roll forming process of anisotropic Al6061 using ductile fracture criteria and FLD

In this research, the fracture phenomenon was investigated on flexible roll forming process of channel section using ductile fracture criteria and forming limit diagram (FLD) by considering the effect of anisotropy. For this purpose, a finite element simulation of the process using the ABAQUS software was done. The fracture in this process was evaluated by considering six types of ductile fracture criteria by UMAT subroutine implementation on the FEM software and using FLD criterion. Experimental tests were performed on 27 blanks of Al6061-T6 using flexible roll forming machine made in Shahid Rajaee Teacher Training University (SRTTU). Numerical results were validated by experimental results. In addition, prediction of occurrence and fracture position by ductile fracture criteria and FLD criterion were compared with experimental results; the Argon criterion was chosen as the most appropriate criterion to predict the fracture position and its occurrence. The fracture occurrence was only observed in a 60° bending angle for 1.5- and 2-mm thicknesses, and the fracture position error percentages of the Argon criterion with experiments for these cases were 18.7 and 3.5%, respectively. Also, the effects of parameters such as sheet thickness, bending radius, and bending angle on the fracture phenomenon by using the selected criterion of Argon were studied.     

断裂力学判据存在的一个问题及讨论

利用细观力学对材料断裂机理的认识，结合脆性材料常规破坏试验结果，提出了一个新的拉断破坏条件，该拉断强度条件与常用的几何脆断强度条件相比，能更好地解释材料在复杂应力状态下发生的脆断与小塑性韧断，并对常用的断裂力学判据存在的问题进行了讨论，通过分析影响裂尖空穴扩张的主要因素，给出能适应不同应力状态的新的断裂判据。     

31Si2MnCrMoVE钢薄板试样表面裂纹断裂韧度测试

31Si2MnCrMoVE钢是为符合固体火箭发动机壳体设计需要而专门研制的超高强度钢。随着冶炼技术的进步,31Si2MnCrMoVE钢断裂韧度不断提高,构件采用的板厚也越来越薄。由于较高的断裂韧度和较小的板厚,给钢板表面裂纹断裂韧度测试带来困难,韧带尺寸偏小,难以满足有效性判据。这种情况下,不应该用线弹性断裂力学方法评价材料的断裂韧度,而应采用弹塑性断裂力学测试材料的延性断裂韧度JIC。基于以上原因,在条件断裂韧度不满足有效性判据的情况下,采用试验与有限元分析相结合的方法,通过试验测出裂纹启裂时的条件载荷,用有限元法计算出在条件载荷作用下的延性断裂韧度JIC,再用断裂力学理论转换成表面裂纹断裂韧度KIe。用JIC作为断裂参量,就必须分析J积分的有效性,因此讨论超高强度钢表面裂纹前缘的J守恒和J主导的有效性,从而为固体火箭发动机设计提供依据。     

Temperature distributions in the high speed drawing of high strength steel wire

High carbon steel wire is known to be susceptible to low-temperature ageing effects, and it is thought that wire properties can be significantly affected by the heat generated during the drawing process. In this paper, the spherical velocity field used in upper bound calculations has been used in conjunction with a model of frictional heating to calculate temperature distributions arising in wire as a result of drawing. The subsequent temperature profiles existing during cooling by direct water quenches are modelled using a commercial finite-element program. Surface temperature histories calculated using the model have been compared with experimental data. The thermal history of the wire during drawing can thus be established, in order to assess the likely effects of strain ageing on the mechanical properties of the wire.     

The fracture toughness behaviour of interpenetrating phase composites

The fracture toughness properties of two interpenetrating phase composites (IPCs)—a bronze-infiltrated porous 420 stainless steel and a polymer resin-impregnated porous 316L stainless steel—have been measured using ASTM Standard E 813-89. Both IPCs exhibited stable crack growth at all volume fractions, resulting from an increase in toughness with crack growth (R-curve behaviour). Initiation toughness, J_Ic, increased and R-curve behaviour became more pronounced with increasing volume fraction of the more ductile constituent phase. R-curve behaviour is attributed to the mechanisms of crack bridging and unloading in the wake of a process zone, which is characterized by secondary cracking and plasticity. The importance of an interpenetrating phase morphology is dependent upon the combination of materials, but it appears that interconnecting the more ductile phase will result in increased toughness, particularly if this is the stronger and stiffer phase. The application of ASTM Standard E 813-89 to the IPCs investigated was found to result in a large number of validity criterion failures. The implications of these failures are discussed.     

基于统一强度理论的断裂准则

基于统一强度理论,在小范围屈服条件下,推导Ⅰ、Ⅱ复合型裂纹裂尖塑性区范围的统一解析解。给出不同拉压比α、泊松比υ、中间主应力影响参数b以及裂纹倾角β下的一族塑性区形状与大小的轨迹,讨论以上参数对裂尖塑性区变化的影响。最后基于裂纹尖端塑性区的解析解,提出了一种复合型裂纹断裂准则,分析了裂纹倾角与初始断裂角的关系。结果表明,该准则预测结果比其它准则更精确,与试验结果吻合得非常好。     

Effect of temperature on crack initiation in gas formed structures

In the gas forming process, the work piece is formed by applying gas pressure. However, the gas pressure and the accompanying gas temperature can result in crack initiation and unstable crack growth. Thus, it is vital to determine the critical values of applied gas pressure and temperature to avoid crack and fracture failure. We studied the mechanism of fracture using an experimental approach and finite element simulations of a perfect aluminum sheet containing no inclusions and voids. The definition of crack was based on ductile damage mechanics. For inspection of initiation of crack and rupture in gas-metal forming, the ABAQUS/EXPLICIT simulation was used. In gas forming, the applied load is the pressure applied rather than the punching force. The results obtained from both the experimental approach and finite element simulations were compared. The effects of various parameters, such as temperature and gas pressure value on crack initiation, were taken into account.     

A study of spur gear pitting formation and life prediction

In this study, a numerical prediction on pitting formation is carried out in spur gear made from austempered ductile iron. General two-dimensional rolling sliding contact situations are considered for the development of the analytical model. The problem is assumed under linear elastic fracture mechanics and the finite element method is used for numerical solutions. Mixed mode stress intensity factors K_I and K_II for cyclic loading are evaluated and related to crack extension by a Paris-type equation. The maximum tangential stress criterion is used to determine the crack-turn-angle during crack propagation under cyclic loading.A series of experimental study is also carried out to determine the pitting formation life. Test specimens were first austenitized in salt bath at 900 °C for 90 min after which they were quenched in salt bath at 325 and 425 °C, for 60 min. A comparison is carried out between numerical and experimental results.     

Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet

Forming limit curves at neck and at fracture have been experimentally determined, and surfaces of fractured dome specimens have been observed optically and in the SEM, for an automotive AA6111-T4 sheet material. Various continuum ductile fracture criteria from the literature along with the assumptions of power law hardening, Hill’s quadratic yield criterion, and proportionality of stress and strain paths have been utilized for prediction of forming limit curve at fracture and compared with the experimental curve to assess the applicability of the different fracture criteria. The maximum shear stress criterion by Tresca predicts reasonably well the fracture limits of AA6111-T4 sheet material for a range of strain ratios, and is consistent with the microstructural observations. The criterion can be used to predict fracture limit curves from uniaxial tensile data and plane strain limit at fracture. A methodology for incorporating such a ductile fracture criterion into FE simulations of sheet stampings for prediction of fracture is discussed.     

A prediction of bursting failure in tube hydroforming processes based on ductile fracture criterion

Bursting is an irrecoverable failure mode in tube hydroforming, in contrast with buckling and wrinkling. To predict bursting failure in the hydroforming processes, Oyane's ductile fracture criterion is introduced and evaluated from the results of stress and strain productions obtained from finite element analysis. The region of fracture initiation and the bursting pressures are predicted and compared with a series of experimental results. It is shown that the material parameters used in the criterion can be obtained from the forming limit diagram. From the simulation results of tube bulging, the prediction of the bursting failure based on the ductile fracture criterion was demonstrated to be reasonable. This approach can be extended to a wide range of practical tube hydroforming processes.     

筒形件液压拉伸工艺的计算机辅助分析

开发了筒形件液压拉伸工艺的计算机辅助分析程序，该程序能模拟筒形件的液压拉伸过程，计算工件各部位在拉伸过程中的应力情况， 从而判断在给定的工艺条件下拉伸过程能否顺利完成。经实验验证， 该程序具有较好的实用性     

Analysis of conical tool perforation of ductile metal sheets

The perforation of a ductile metal sheet with a conical tool is accompanied by elasto–plastic bending, stretching, plastic flow and perforation initiation and propagation and ultimately it results in material fracture in the form of petals. The number and size of petals depends on the sheet thickness, material properties, tool angle, anisotropy in the material and indentation speed. In this work the mathematical relations for the fracture mechanism has been developed to analyze different parameters’ response and evaluate fracture toughness of the metal sheets of various thickness using computer code based on this analysis.