聚碳酸脂板快速扩展裂纹的弹塑性研究

本文实验观察研究了聚碳酸脂板Ⅰ型裂纹失稳扩展的特征.由修正的 Dugdale 窄带屈服模型,用实验-数值计算混合法确定了动态延性裂纹顶端附近的应力场参数.理论计算与实验测定结果相符合.本文的工作对研究延性断裂机理及裂纹扩展准则的研究是有意义的.     

裂纹端部塑性区修正公式的改进——对Irwin模型的修正

对于小范围屈服断裂,必须进行塑性区修正,为此,Irwin G.R.,Dugdale D.S.等人先后提出了简化该问题研究的模型和处理方法,鉴于Irwin模型的不甚合理,本文对它提出了一个修正方案,使之较为合理和精确。计算结果表明,修正后的模型比原Irwin模型更接近于公认较精确的Dugdale模型。我国新编的材料力学教材中,都介绍了Irwin模型,采用了Irwin G.R.关于塑性区修正的观点与结果。而且,“由于平面应力状态塑性区较宽,必须进行修正。”可见,对该模型存在的问题进行讨论和改进实有必要。     

平面应力的弹塑性断裂模型及其有限元分析

本文根据文献对薄钢板试样的实验分析,提出一个平面应力的弹塑性断裂模型——带状颈缩区模型.将Dugdale模型推广到弹塑性变形场情形.用弹塑性全量理论和增量理论的有限元法,分别计算了具有中心裂纹的薄宽板受均匀拉仲情形的裂纹张开位移、应力应变场.结果表明Burdekin设计曲线在一定条件下才是安全的,本文计算的裂纹张开位移与一些实验测量结果符合良好.     

Dugdale模型与压力容器长表面裂纹的CTOD

本文把压力容器长表面裂纹简化为狭长条的单边裂纹。利用Dugdale模型和二维混合边值问题的奇异积分方程解法,计算了在均匀拉伸和纯弯曲两种载荷下,裂纹尖端前沿的韧带区没有完全屈服时的裂纹尖端张开位移CTOD。最后介绍如何把计算结果应用到工程实际问题。     

非晶态高聚物裂尖银纹损伤场

在非晶态高聚物裂端塑性区引入银纹损伤，提出了一个修正的Dugdale模型，并由它确定塑性区的大小，算例表明，银纹损伤导致了塑性区深度的增加。此外，在Dugdale模型下研究了稳态扩展的端塑性区，在裂纹缓慢扩展、小范围银纹化以及材料为线粘弹性等假定下，由能量原理得到了控制裂纹生长的一个非线性微分一积分方程，从中看到银纹损伤的影响十分显著。     

用有限元法分析粘弹性体的断裂

本文基于Dugdale模型,采用有限元法计算粘弹性体裂纹扩展的规律,沿裂纹方向逐步脱开结点以模拟裂纹的扩展。计算中应用增量叠加的方法,算例表明,有限元计算的从加载起至裂纹开始扩展的孕育时间和裂纹扩展速度与解析解较好地符合。     

哈密顿体系在断裂力学Dugdale模型中的应用

利用平面扇形域哈密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于Dugdale模型的平面裂纹弹塑性解析元列式。将该解析元与有限元相结合，构成半解析的有限元法，可求解任意几何形状和荷载平板裂纹的Dugdale模型问题。数值计算结果表明本文方法对该类问题的求解是十分有效的，并有较高的精度。     

考虑材料强化时小范围屈服理论

在准脆性裂纹情况下,裂纹尖端附近存在的小范围屈服区的影响是不能忽略.本文讨论了裂纹长度和外加应力同时改变,并考虑材料强化效应后的小范围屈服理论.文中引用了五种不同的方法进行了计算与比较.     

含裂绞加劲板在轴向载荷作用下的弹塑性分析

本文应用Dugdale模型实现了含裂纹加劲板在轴向载荷作用下的弹塑性分析,结果与应用Dugdale塑性特性的有限元解十分符合,两者误差在3％以内。     

用可动节点有限元模型模拟裂纹扩展过程

本文针对裂纹扩展有限元模拟模型存在的问题,提出一种可动节点模型.使裂尖在单元尺度内任意移动,实现了扩展模拟连续性.加进松弛扩展,突出其所占比重,使模拟更加逼真.用弹塑性有限变形杂交元自编模拟裂纹扩展的通用FORTRAN 程序,对含中心裂纹铝板进行模拟,假定材料各向同性并遵守等向强化规律,采用米赛斯屈服准则和Drucker 塑性势流动理论做增量弹塑性静力分析,得到了与实验符合较好的结果.     

Nonlinear fracture of 2D magnetoelectroelastic media: Analytical and numerical solutions

A strip electric–magnetic polarization saturation (SEMPS) model is developed to study the electric and magnetic yielding effects on a crack in magnetoelectroelastic (MEE) media. In this model, the MEE medium is treated as being mechanically brittle, and electrically and magnetically ductile. Analogously to the classic Dugdale model, the electric and magnetic yielding zones in front of the crack are represented for simplicity by two strips. In the electric yielding strip the electric displacement equals the electric displacement saturation and meanwhile in the magnetic yielding zone the magnetic induction equals the magnetic induction saturation. The nonlinear analytical solution of this SEMPS model of crack in an infinite MEE medium is obtained using an integral equation approach. The equivalence between the proposed SEMPS model and the existing strip electric–magnetic breakdown (SEMB) model is demonstrated.To analyze the nonlinear fracture problem in the corresponding finite MEE media, the non-linear hybrid extended displacement discontinuity-fundamental solution (NLHEDD-FS) method is modified, and a multiple iteration approach is adapted to determine the electric and magnetic yielding zones. Comparing with the analytical solution, the applicability and effectiveness of the NLHEDD-FS method is verified. Numerical results based on the SEMPS model for a center crack in infinite and finite MEE strip are presented.     

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

Residual strength of a fiber reinforced metal matrix composite with a crack

The residual strength of a cracked unidirectional fiver reinforced metal matrix composite is studied. We propose a bridging model based on the Dugdale strip yielding zones in the matrix ahead of the crack tips that accounts for ductile deformations of the matrix and fiber debonding and pull-out in the strip yielding zone. The bridging model is used to study the fracture of an anisotropic material and its residual strength is calculated numerically. The predicted results for a SiC/titanium composite agree well with the existing experimental data. It is found that a higher fiber bridging stress and a larger fiber pull-out length significantly contribute to the composite's residual strength. The composite's strength may be more notch-insensitive than the corresponding matrix material's strength depending on several factors such as fiber-matrix interface properties and the ratio of the matrix modulus to an ‘effective modulus’ of the composite.     

The ductile fracture of polycarbonate

The fracture of a known ductile polymer (polycarbonate) is investigated. It is shown that polycarbonate obeys the Dugdale model of ductile yielding by comparing measured plastic-zone sizes and displacements to the theoretical predictions. Strain-energy release rates are calculated and the critical value is shown to be one or two orders of magnitude higher than critical values for brittle polymers. Photoelastic photographs of the fracture process are presented and it is shown that the photoelastic effect definitely enhances the definition of the yield zone. Microscopic photoelastic photographs are also presented which are used to give a new interpretation to the photoplastic effect. Finally, suggestions for future work are presented.     

Overall damage and elastoplastic deformation in fibrous metal matrix composites

A phenomenological constitutive model for fibrous composite materials with a ductile matrix is postulated incorporating damage mechanics with micromechanical behavior. The model is first formulated in an undamaged composite system and then transformed consistently achieved in terms of an overall damage tensor M for the whole composite. In the process of formulating this model, interesting results are obtained demonstrating the necessity of using a non-associated flow rule for plasticity in the damaged composite system together with a Hill's type yield criterion. It is also shown that using a Ziegler-Prager kinematic hardening rule for the ductile matrix leads to a general kinematic hardening rule for the composite that is a combination of a generalized Ziegler-Prager model and a Phillips-type model. Finally, an explicit expression for the elastoplastic stiffness tensor for the damaged composite is obtained.     

Crack-opening displacements and normal strains in centrally notched plates

Experimentally determined crack-opening displacements of stationary and running cracks and of inclined stationary cracks in centrally notched plates are reported in this paper. The moiré-fringe technique was used for the determination of displacement fields in test specimens of magnesium, 7075-T6 and 7178-T6 aluminum alloys. Experimentally determined crack-opening displacements were compared with corresponding re ults based on theoretical models of Westergaard, Dugdale, Craggs and Craggs-Dugdale. In addition, normal-strain fields derived from the moiré-fringe data were compared with static or dynamic strain fields of these theoretical models. The results of this investigation indicate that while the Dugdale crack is a fair model of a stationary crack in ductile materials, the Craggs crack appears to be a better representation of a running crack in the ductile materials investigated.     

Further studies on crack-tip plasticity of rapid tearing

A modified Dugdale model for rapid tearing is reviewed. Further justification of the model is provided by agreements between the measured crack-tip-opening displacement in rapidly tearing polycarbonate specimens and those computed by using the model. The model is then used to determine the residual stresses in an unloaded polycarbonate fracture specimen after crack arrest. The modified Dugdale model is also used to analyze the rapid tearing data of aluminum fracture specimens.     

Deformation and the strip necking zone in a cracked steel sheet

When a tensile stress is applied to a thin cracked plate, a strip necking region results ahead of a crack tip. The relative opening displacement between the crack surfaces and between the upper and lower boundaries of the strip necking region were measured by the moiré method. The strains ahead of the strip necking region and the thickness reduction (therein) were also measured. The measured relative opening displacements were compared with the calculated values using the Dugdale strip necking model. The thickness reduction in the strip necking region is equal to the relative opening displacement.     

A computational model of viscoplasticity and ductile damage for impact and penetration

A coupled constitutive model of viscoplasticity and ductile damage for penetration and impact related problems has been formulated and implemented in the explicit finite element code LS-DYNA. The model, which is based on the constitutive model and fracture strain model of Johnson and Cook, and on continuum damage mechanics as proposed by Lemaitre, includes linear thermoelasticity, the von Mises yield criterion, the associated flow rule, non-linear isotropic strain hardening, strain-rate hardening, temperature softening due to adiabatic heating, isotropic ductile damage and failure. For each of the physical phenomena included in the model, one or several material constants are required. However, all material constants can be identified from relatively simple uniaxial tensile tests without the use of numerical simulations. In this paper the constitutive model is described in detail. Then material tests for Weldox 460 E steel and the calibration procedure are presented and discussed. The calibrated model is finally verified and validated through numerical simulations of material and plate perforation tests investigated experimentally.     

Crack tip field in a linear elastic–plastic strain-hardening material

The strip necking model for strain-hardening materials is studied in this paper, in which the stress distributed over the strip necking zone is assumed to be ultimate stress. The bi-linear stress–strain relation which can model certain features of plastic flow is adopted in this model. The stress and strain fields are calculated based on this model in this paper. The size of the strip necking region is determined by balancing the stress intensity factor due to remote loading with that due to assumed closing forces equal to the ultimate tensile strength of the material distributed over the strip necking zone. It is interesting that the strip necking region size and the crack tip opening displacement depend not only on the remote load, but also the material hardening parameters, which is different from the results of strip yield model. The results agree with experiments well, and the model has wider application.