孔洞敏感超塑性材料变形的数值分析

本文用两种数值方法,非线性长波分析和刚粘塑性有限元方法研究了孔洞敏感的超塑性材料在单向拉伸和园板涨形中的不均匀变形和断裂过程。分析表明,这种过程是不均匀几何失稳与内部孔洞长大的结合与相互作用的结果。材料的应变速率敏感性指数与孔洞长大速率通过不同的变形机理图控制着这种过程。叠加的静水压力能够改变孔洞敏感材料的断裂模式,从常压下没有宏观颈缩的孔洞断裂到无内部孔洞的外部颈缩断裂。     

Effect of strain rate sensitivity and cavity growth rate on failure of superplastic material

Abstract

Necking development and fracture strain of superplastic material under tensile load are analysed by introducing a model of cavity growth into the long wavelength approximation analysis which can describe the external neck development of specimens during deformation. The results show that both strain rate sensitivity m and cavity growth rate η have an important influence on the fracture strain of superplastic material. According to these results, a fracture diagram is presented in m–η coordinates, which is divided into three: a region in which material fails by macroscopic external necking, a region where cavity growth is predominant leading to fracture without pronounced external necking, and an intermediate region where both fracture modes occur. The prediction of fracture strain for various superplastic alloys exhibiting cavity growth during deformation is in good agreement with experimental results. The present analysis thus enables quantitative prediction of the effects of both strain rate sensitivity and cavity growth on superplastic fracture under uniaxial tension.

MST/491     

Effect of stress state on cavitation and hole growth in superplastic AA 7475 aluminium alloy

Abstract

A study has been made of the growth of cavities and of artificial holes in AA 7475 alloy sheet material during both uniaxial and equibiaxial tensile straining, with the object of clarifying the effect of stress state on cavitation during superplastic flow. The growth rate of cavities with strain was observed to be lower for uniaxial tension than for equibiaxial tension. An analysis of artificial hole growth data supports these observations, and is consistent with the view that continuous cavity nucleation and cavity coalescence lead to an increase in the apparent cavity growth rate during superplastic flow.

MST/1149     

Failure analysis on gas pressure formed spherical domes of Pb–Sn eutectic alloy

Abstract

This paper addresses the issue of instability of deformation during gas pressure forming of superplastic sheets. With regard to fracture strain, the plastic behaviour of the spherical dome has been described in terms of the local effective stress and the effective strain. These quantities are equated to the uniaxial stress state. The limiting effective thickness strain is obtained utilising the relations between the strain rate sensitivity index and the fracture strain. The results are found to be in good agreement with the measured failure strains.     

An analysis of deformation and failure in rectangular tensile bars accounting for void shape changes

A three-dimensional finite deformation study of necking and failure in rectangular tensile bars is carried out using a constitutive relation for porous material plasticity. The fully dynamic formulation accounts for void nucleation and growth along with thermal and rate effects, but here focus is on quasi-static response with a specified initial void volume fraction. The constitutive relation takes into account void shape changes and associated void rotations for three-dimensional voids. The constitutive update is carried out using a generalized rate tangent scheme for an elastic-viscoplastic solid. The sensitivity of necking and failure patterns to the aspect ratio of the rectangular bar is investigated with focus on the plane strain limit and a square tensile bar. The calculations predict the well-known slant fracture in plane strain tension and the emergence of a cup-cone like failure region for a square cross-section. Details are provided for the development of porosity in the bar with a square cross-section, including void shape changes and void rotations. The numerical examples show the capability of a constitutive relation for porous plasticity that can model details of void evolution, thus paving the way for advanced analyses of ductile failure under arbitrary loadings.

     

Determination of Ductile Fracture Parameters of a Dual‐Phase Steel by Optical Measurements

Marciniak–Kuczynski and Nakajima tests of the dual‐phase steel Docol 600DL ( www.ssab.com/ ) have been carried out for a range of stress‐states spanning from uniaxial tension to equi‐biaxial tension. The deformation histories of the specimens have been recorded by digital images, and the displacement and strain fields have been determined by post‐processing the images with digital image correlation software. The fracture characteristics of the material are presented by means of the stress triaxiality, the Lode parameter and the equivalent strain. These parameters are evaluated on the surface of the specimens based on the optical field measurements and assumptions regarding the mechanical behaviour of the material. Additionally the minor versus major principal strains up to fracture are presented. It is found that the material displays a significantly lower ductility in plane‐strain tension than in uniaxial tension and equi‐biaxial tension, and that it, in the tests exposed to local necking, undergoes large strains between the onset of necking and fracture. Fractographs of selected specimens reveal that fracture is due to growth and coalescence of voids that occur in localised areas governed by shear‐band instability.     

Tensile deformation behaviour of high isotactic polypropylenes

Abstract

The tensile flow behaviour and deformation processes during uniaxial loading of high isotactic (high crystallinity) polypropylenes have been investigated at various strain rates. The strain rate sensitivity index indicated that long chain high isotactic (high crystallinity) polypropylene (iPP-L) is relatively less sensitive to strain rate than short chain high isotactic (high crystallinity) polypropylene (iPP-S). Deformation bands formed at low strain contributed to the separation of fibrils/microfibrils, and on subsequent increase in tensile strain, the deformation bands developed into an array of closely spaced crazes that multiplied with an increase in strain and strain rate, and grew inwards. Three fracture morphologies were identified in iPP-L: brittle fracture, crazing - tearing, and brittle fracture with ductile pulling of fibrils/microfibrils (quasi-cleavage). In iPP-S, the predominant mode of failure at all displacement rates was brittle fracture. However, at lower displacement rates, smooth and circular voids associated with nucleating particle were randomly present on the brittle fracture surface of iPP-S. Occasional wedges were also observed on the tensile deformed surface of iPP-S. The deformation processes have been depicted in terms of strain rate - strain deformation diagrams.     

Forming and fracture limits of aluminium alloy

Abstract

Forming and fracture limits of an AA 3104-H19 aluminium alloy sheet were studied by hydraulic bulging and Marciniak type deep drawing and tensile tests. The alloy appeared to be highly anisotropic, exhibiting distinctly different fracture patterns in the rolling and transverse directions. The preferred fracture direction was transverse to the rolling direction. In the tensile test, samples loaded in the rolling direction failed transverse to the rolling direction, but in the transverse direction, the fracture was inclined at ～55° to the tensile axis. In some cases, two such competing fractures in the characteristic directions could be observed. Scanning electron microscopy studies revealed a typical ductile fracture pattern. The fracture occurred by shearing in the through thickness direction, and typical alternating shear lips in a direction inclined at ～45° to the through thickness direction could be observed. Forming limit diagrams for both rolling and transverse directions were determined from the experiments. The measured limit strains in uniaxial tension were predicted well by the modified Rice–Tracey theory, but in equibiaxial tension, the theory overestimated the fracture limit strains.     

Evaluation of threshold stress intensity in high strength hydrogen charged steel in low strain rate tension tests

Abstract

The fracture ductility of high strength steel is strongly influenced by the presence of hydrogen, although hydrogen does not significantly affect the yield strength. The deterioration of fracture ductility is particularly evident in low strain rate tension tests, but less pronounced at conventional crosshead speeds. Low concentrations of hydrogen in high strength steels do not substantially affect the fracture toughness, but result in the appearance of a threshold stress intensity. The threshold values can be obtained from low strain rate tension tests at a crosshead speed of 0·1 mm min^?1. These values are practically the same as those obtained from hydrogen charged peripherally notched pre cracked specimens subjected to a constant static load in a delayed failure test. Microfractographic investigations of fracture surfaces of hydrogen charged steel from low strain rate tension tests indicate that the growth and the coalescence of voids in the final stages of the fracture process are partly assisted by the decohesion of interfaces on which hydrogen is adsorbed.

MST/1796     

Prediction of non-uniform thinning in superplastically formed spherical domes

Abstract

Superplastic forming is an attractive manufacturing process, which allows the production of complex sheet metal components. The gas pressure bulging of metal sheets has become an important forming method. As the bulging process progresses, significant thinning in the sheet material becomes obvious. A prior knowledge about non-uniform thinning in the product after forming helps the designer in the selection of initial blank thickness. This paper suggests a simple procedure to obtain the variation in thickness of a gas pressure formed spherical dome at any instant of time during the bulging process. This simple procedure is validated by comparing predicted and measured thicknesses of a formed titanium hemispherical dome.     

Hot tensile deformation behaviors and constitutive model of an Al–Zn–Mg–Cu alloy

The hot tensile deformation behaviors of an Al–Zn–Mg–Cu alloy are studied by uniaxial tensile tests under the deformation temperature of 340–460 °C and strain rate of 0.01–0.001 s⁻¹. The effects of deformation temperature and strain rate on the hot tensile deformation behaviors and fracture characteristics are discussed in detail. The Arrhenius-type constitutive model is developed to predict the peak stress under the tested deformation condition. The results show that: (1) The true stress–true strain curves under all the tested deformation conditions are composed of four distinct stages, i.e., elastic stage, uniform deformation stage, diffusion necking stage and localized necking stage. The flow stress decreases with the increase of deformation temperature or the decrease of strain rate. (2) The elongation to fracture increases with the increase of deformation temperature. Under the tested conditions, the strain rate sensitivity coefficient varies between 0.1248 and 0.2059, which indicates that the main deformation mechanism is the lattice diffusion-controlled dislocation climb. (3) The localized necking causes the final fracture of specimens under all the deformation conditions. Microvoids coalescence is the main fracture mechanism under relatively low deformation temperatures. With the increase of deformation temperature, the intergranular fracture occurs. (4) The peak stresses predicted by the developed model well agree with the experimental results, which indicate the validity of the developed model.     

Numerical analysis of effect of material and processing parameters on thickness distribution during superplastic die bulging of cavity sensitive materials

Abstract

The superplastic bulging of circular sheets clamped against axisymmetrical cylindrical dies has been analysed numerically by means of a rigid–viscoplastic finite element method, in which four node quadrilateral isoparametric elements are used with a Newton–Raphson non­linear solution scheme. Both effects of normal anisotropy and strain hardening in the material are considered and a modified Coulomb friction law is adopted. At the same time, the yield criterion suited for the superplastic forming process and the cavity damage evolution model deduced from continuum damage mechanics are applied to a finite element formulation. The influences of material parameters (the strain rate sensitivity exponent m, the strain hardening exponent n, the coefficient of normal anisotropy R) and processing parameters (pressure cycle, lubrication condition, die geometry) on the inhomogeneity of the thickness distribution are studied and discussed. A selection of the simulated results is compared with the experimental results, with good agreement.     

低碳钢薄壁焊管液压胀形行为

为了研究焊管液压胀形过程的变形行为,在管材胀形性能测试系统上进行了不同长径比条件下低碳钢(STKM11A)薄壁焊管的胀形实验,获得了焊管的壁厚分布规律、胀形区轮廓形状、极限膨胀率和应变分布规律。结果表明:管材焊缝区的减薄率仅为2.4%~5.5%,等效应变仅为0.05~0.10,变形程度相对母材区较小,主要发生几何位置移动。环向壁厚的最薄点位于以焊缝为中心的对称两侧士30°位置处。随着胀形区长度增大,管材破裂压力、减薄量、极限膨胀率均发生减小,胀形区轮廓逐渐偏离椭圆形,当长径比达到2.0时,已不再适合用椭圆函数描述。此外,胀形区长度增大过程中,管材从双拉向平面应变状态发生转变,在此基础上建立了焊管的成形极限图。     

Effect of inverted pressurisation profile on deformation characteristics of 5083 aluminium alloy during superplastic forming

Abstract

Decreasing the cycle time for superplastic forming of a commercially available superplastic 5083 aluminium alloy has been studied in the present work by use of an inverted pressurisation profile. A right cylindrical cup with a depth/ diameter ratio of 0·5 could be superplastically gas pressure formed in less than 100 s. The deformation behaviour was similar to that of constant strain forming during the free bulging stage. In this stage, a stress state gradient from the pole to the edge of the formed dome was observed. Plasticity controlled growth of cavities was thought to be the mechanism for the increase of cavity volume fraction during forming. After the centre point of the deformed sheet touched the die surface, the metal flow pattern was found to be different from that of the traditional approach. The minimum thickness was not located at around the bottom corner of the cylindrical cup rather it was located ~ 7.5 mm away from the bottom centre of the cup with radius 20 mm. Significant cavity nucleation and coalescence caused higher cavity growth rates at large strains, owing to the continuous increase in strain rate resulting from the imposed pressurisation profile.     

EFFECT OF BIAXIAL MEAN STRESS ON CYCLIC STRESS-STRAIN RESPONSE AND BEHAVIOUR OF SHORT FATIGUE CRACKS IN A HIGH STRENGTH SPRING STEEL

Abstract— Biaxial fatigue tests were conducted on a high strength spring steel using hour-glass shaped smooth specimens. Four types of loading system were employed, i.e. (a) fully reversed cyclic torsion, (b) uniaxial push—pull, (c) fully reversed torsion with a superimposed axial static tension or compression stress, and (d) uniaxial push—pull with a superimposed static torque, to evaluate the effects of mean stress on the cyclic stress—strain response and short fatigue crack growth behaviour. Experimental results indicate that a biaxial mean stress has no apparent influence on the stress—strain response in torsion, however a superimposed tensile mean stress was detrimental to torsional fatigue strength. Similarly a superimposed static shear stress reduced the push—pull fatigue lifetime. A compressive mean stress was seen to be beneficial to torsion fatigue life. The role of mean stress on fatigue lifetime, under mixed mode loading, was investigated through experimental observations and theoretical analyses of short crack initiation and propagation. Using a plastic replication technique the effects of biaxial mean stress on both Stage I (mode II) and Stage II (mode I) short cracks were evaluated and analysed in detail. A two stage biaxial short fatigue crack growth model incorporating the influence of mean stress was subsequently developed and applied to correlate data of crack growth rate and fatigue life.     

Comparisons of deformation and fracture behaviour of PC/ABS blend and ABS copolymer under dynamic shear loading

Abstract

The dynamic shear deformation and fracture characteristics of PC/ABS blend and ABS copolymer with regard to the relation between mechanical properties and strain rate, are studied experimentally using a torsional split Hopkinson bar at room temperature under strain rates ranging from 8 × 10² s^-1 to 3.4 × 10³ s^-1. Fracture phenomena are analysed by scanning electron microscopy and correlated with macroscopic behaviour. The relative properties and fracture mechanism of both polymers are also compared. Results show that strain rate enhances shear strength of both PC/ABS blend and ABS, but fracture shear strain tends to decrease with increasing strain rate. ABS exhibits better ductility and lower shear strength. For both polymers, strain rate sensitivity increases with increasing range of strain rate, while an inverse tendency occurs for activation volume. Higher strain rate sensitivity and lower activation volume are found in PC/ABS blend. PC/ABS blend fracture is dominated by mixed shearing and tearing, but ABS fracture shows only shearing. Due to the increasing deformation heat, fracture surface viscoplastic flow for both polymers increases with increasing strain rate, inducing lower flow resistance and lower fracture strain at higher stain rates. The viscoplastic flow behaviour in ABS is more active.     

Response of titanium alloys to high strain rate deformation

Abstract

The stress-strain response of samples of Ti64 and Ti550 at strain rates from 10^?1 s^?1 to 10³ s^?1 and samples of Ti811 and Ti153 at a strain rate of 10³ s^?1 have been assessed. It has been found that the influence of the imposed strain rate on the stress-strain response of Ti64 and Ti550 alloys is very similar – in both alloys the yield stress increases with increase of strain rate and the energy absorbed to fracture increases. At high strain rates localised deformation occurs in the form of shear bands in Ti64 and Ti550 but no shear banding was seen in Ti811 and Ti153. The fracture surfaces of Ti64 and of Ti550 show an increased tendency to brittle failure and an increase in necking with increase of strain rate. The influence of alloy microstructure and composition on the response to changes in imposed strain rate are discussed in terms of adiabatic heating and the factors controlling the flow stress in these alloys.     

A Closer Look at the Diffuse and Localised Necking of A Metallic Thin Sheet: Evolution of the Two Bands Pattern

Plastic strain localisation in a sheet specimen was monitored by electronic speckle pattern interferometry during uniaxial tensile tests. The experiments were carried on in the diffuse and localised necking stages until fracture. A kinematic model, which is independent of material characteristics, was used to describe the whole strain rate field with two crossing localisation bands inclined with respect to the tensile direction. Then, the physical features of localisation, such as the width of the two bands, their inclination angles and their maximum strain rates are identified by least‐square from the displacements fields and their evolutions are followed from the onset of diffuse necking up to the failure. In particular, the effect of the average strain rate is considered and bandwidth evolution is analysed in detail. It was found that:

• The band structure appears early, as soon as diffuse necking starts;
• The separation, in terms of strain rate or bandwidth, of the two bands corresponds to the transition between diffuse and localised necking. The localised necking stage can be divided into two sub‐stages: in the first one, the two bands continue to evolve but at different rates, and in the second one, one of the bands stabilises. The transition between the two sub‐stages is influenced by the crossbeam velocity;
• The inclination of the band leading to fracture remains quite stable, while the other rotates towards a situation perpendicular to the tensile direction;
• The band width decreases exponentially versus the maximum local strain. The two bands follow the same evolution path, but one of them progressively lags behind the other until it stops deforming.
• Although the average strain rate was only varied by a factor two, it was found that, when the strain rate increases, the two bands stay together longer and thus that the onset of localised necking is delayed.

     

Investigation of process zone structure in Fe–3Si alloy

Abstract

An in situ fracture experiment was carried out in a scanning electron microscope to investigate plastic deformation and strain distribution in the process zone (PZ) located in the immediate vicinity of the crack tip in an Fe–3Si alloy (wt-%) under mixed mode loading conditions. It was observed that plastic deformation occurred by successive activation of a number of slip systems. The strain distribution and shape of the PZ were strongly dependent on the crystallographic orientation of the grain containing the crack tip. The distribution differed from that predicted using near tip blunting calculations and was best expressed by an exponential equation. Additional strain concentrations created by surface defects caused slight perturbations in the overall distribution. Crack propagation started along a coarse slip band which possessed the highest strain. It was found that the maximum strains in the PZ exceeded the uniaxial tensile fracture strain.

MST/1404     

Hot tensile deformation behaviors and constitutive model of 42CrMo steel

The hot tensile deformation behaviors of 42CrMo steel are studied by uniaxial tensile tests with the temperature range of 850–1100 °C and strain rate range of 0.1–0.0001 s⁻¹. The effects of hot forming process parameters (strain rate and deformation temperature) on the elongation to fracture, strain rate sensitivity and fracture characteristics are analyzed. The constitutive equation is established to predict the peak stress under elevated temperatures. It is found that the flow stress firstly increases to a peak value and then decreases, showing a dynamic flow softening. This is mainly attributed to the dynamic recrystallization and material damage during the hot tensile deformation. The deformation temperature corresponding to the maximum elongation to fracture increases with the increase of strain rate within the studied strain rate range. Under the strain rate range of 0.1–0.001 s⁻¹, the localized necking causes the final fracture of specimens. While when the strain rate is 0.0001 s⁻¹, the gage segment of specimens maintains the uniform macroscopic deformation. The damage degree induced by cavities becomes more and more serious with the increase of the deformation temperature. Additionally, the peak stresses predicted by the proposed model well agree with the measured results.