混凝土结构Ⅰ型裂纹裂尖塑性区研究

应用双剪统一强度理论,研究了Ⅰ型裂纹的塑性变形问题。给出了包含反映材料拉压性能差异的参数拉压比及反映中间主应力效应的参数b的Ⅰ型裂纹裂尖塑性区形状和大小的统一解。已有的Tresca准则、Mises准则和Mohr-Coulomb准则解均是本文的特例或线性逼近。针对混凝土结构,画出了不同参数b情况下的裂尖塑性区半径变化图。得出了材料拉压比对Ⅰ型裂纹裂尖塑性区影响很大。b对Ⅰ型裂纹裂尖塑性区影响随拉压比的不同而不同,拉压比较大时,b对塑性区影响大,拉压比较小时,b对塑性区影响小的结论。该统一解可以适应于各种不同材料,能充分发挥材料潜力,具有普遍性和广泛的适应性,有一定的工程应用价值。结论对于研究各种材料的断裂问题有参考作用。     

Ⅲ型过载对调质钢Ⅰ型疲劳裂纹扩展门槛的影响

研究了不同参数的Ⅲ型过载对近门槛区调质40Cr钢Ⅰ型疲劳门槛的影响.结果表明:过载后疲劳门槛均会提高,其程度随过载比的加大而增加;过载次数的有限增多也会使疲劳门槛略有增加,但效果将逐渐趋于饱和.过载机制主要有裂尖尾部塑性诱导裂纹闭合和裂尖附近的残余压应力状态.     

Ⅲ型这载对调质钢Ⅰ型疲劳裂纹扩展门槛的影响

研究了不同参数的Ⅲ型过载对近门槛区调质40Cr钢Ⅰ型疲劳门槛的影响。结果表明：过载后疲劳门槛均会提高，其程度随过载比的加大而增加；过载次数的有限增多也会使疲劳门槛略有增加，但效果将逐渐趋于饱和。过载机制主要有裂尖尾部塑性诱导裂纹闭合和裂尖附近的残余压应力状态。     

基体裂纹-异型夹杂相互作用焦散线实验研究

该文通过透射式静态焦散线方法利用三点弯曲梁断裂实验对异型夹杂与基体裂纹的相互作用进行研究。首先得到不同夹杂情况下I型裂纹尖端的焦散斑图,引入焦散斑纵横轴长之比β反映焦散斑在夹杂作用下的畸变特性;其次,提取相应的焦散斑特征尺寸,并得到I型裂纹的应力强度因子K_I;最后,基于不同夹杂情况下裂尖焦散斑、裂尖应力强度因子与裂尖和夹杂之间距离的关系,揭示不同夹杂对裂纹尖端应力场奇异性影响规律。实验研究结果为含异型夹杂结构的强度设计和断裂性能评估提供实验依据。     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

混凝土Ⅰ型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

基于线性强化模型的双层厚壁圆筒极限内压统一解

基于双剪统一强度理论与双线性强化模型,考虑材料拉压强度的不同及中间主应力效应的影响,推导了均匀内压作用下双层厚壁圆筒的弹、塑性极限内压解,分析了强化模量系数、拉压强度比、统一强度理论参数、内外半径比及分层半径对弹、塑性极限内压统一解的影响。结果表明:随着外径与内径之比的增大,弹、塑性极限内压增加,随着统一强度理论参数的增大,其值增加,随着拉压强度比的增大,其值减小;弹性极限内压与强化模量系数的取值无关,塑性极限内压随着强化模量系数的增大而增加;内外筒的分层半径对弹性极限内压有显著影响,而对塑性极限内压的影响较小。工程应用中,应选择较为合理的壁厚,使其在安全的基础上承受更大的内力;应充分考虑材料中间主应力及拉压强度比的影响,更准确的计算其受力情况,充分发挥材料的潜能。     

不同拉压模量及软化特性材料的柱形孔扩张问题的统一解

对于具有不同的拉压模量及软化特性的岩土类材料,提出了不同拉压模量及软化特性的控制参数,采用双剪统一强度理论推导了柱形孔扩张问题的应力及位移的统一解。分析了模量、模型和软化等控制参数对柱形孔扩张时的扩张压力、塑性区开展规律及应力场的影响。结果表明:圆孔极限扩张压力、塑性区的发展规律、应力场、位移场等均随着模量控制参数、模型参数及软化参数的变化而变化,因此若采用经典的弹性理论、单一的模型参数及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

不同拉压模量及软化特性材料的球形孔扩张问题的统一解

对于具有不同的拉压模量及软化特性的岩土类材料,提出了不同拉压模量及软化特性的控制参数,采用双剪统一强度理论推导了球形孔扩张问题的应力及位移的统一解。分析了模量、模型和软化等控制参数对球形孔扩张时的扩张压力、塑性区开展规律及应力场的影响。结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量控制参数、模型参数及软化参数的变化而变化,因此若采用经典的弹性理论、单一的模型参数及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

挤密桩爆扩成孔及夯填过程的塑性分析

应用统一强度理论,对挤密桩的爆扩成孔和夯实两个阶段进行了塑性分析,得出了土体爆扩成孔塑性边界比例半径计算公式和土体夯填塑性影响比例半径计算公式。所得公式考虑了不同拉压比的影响和中间主应力的影响,可以合理地得出不同材料的相应解,它既适用于拉压强度相等的材料,也适用于拉压强度不相等的材料。这些公式可以适用于各种土体的爆扩塑性影响区的计算和夯实塑性影响区的计算,可以用于分析桩的爆扩是否造成邻桩已夯实的土体的破坏,可以用于分析夯实土体所需的重锤的能量,从而确定重锤的重量和夯击次数。     

Unified triaxiality at the crack tip subjected to plane strain condition under mixed‐mode (I + II) fracture

The new model of stress triaxiality, subjected to plane strain condition under mixed‐mode (I + II) loading, at the yield loci of the crack tip, has been formulated using unified strength theory. It evaluates critical values of triaxiality for various convex and non‐convex failure criteria, unlike the existing model. It shows the effects of Poisson's ratio and intermediate principal stress for materials whose strength in tension and compression is either equal or unequal. Further, on this basis, the crack initiation angles are predicted for various crack inclinations and compared with those obtained from other fracture criteria. The plastic zone shapes supplement the results. Critical yield stress factor, a significant parameter at the crack tip got lowered as the difference among the three principal stresses reduced to a minimum. The crack initiation angles obtained from the model showed good agreement with those obtained from G‐, S‐, and T‐criterion.     

双层组合厚壁圆筒弹脆塑性极限内压统一解

基于三剪统一强度准则和弹脆塑性软化模型,考虑材料的脆性软化和中间主应力效应,推导了双层组合厚壁圆筒弹脆塑性极限内压统一解,探讨了粘聚力、内摩擦角、半径比、强度理论参数和中间主应力系数的影响特性,克服了以往基于Tresca屈服准则、Mises屈服准则或双剪强度理论的理想弹塑性解的不足。研究结果表明:中间主应力、材料模型和脆性软化对厚壁圆筒的极限内压均有显著影响。该文所得统一解具有广泛的适用性和理论意义,不但可退化为现有公式,而且还能得到系列化的新解答,对组合厚壁圆筒的设计及工程应用有重要参考价值。     

GM屈服准则求解Ⅰ型裂尖塑性区

用几何中线(GM)屈服准则求解了Ⅰ型裂尖塑性区的形状与尺寸,对比了基于Mises和Tresca准则的求解结果。表明在平面应变条件下,GM准则求解的塑性区面积在Tresca和Mises结果之间,Tresca塑性区面积最大,Mises面积最小,GM塑性区与Mises塑性区非常接近,三者的塑性区均成哑铃状。在平面应力下,GM和Mises塑性区二者仍最接近并为豆芽状,Tresca的塑性区最大。无论平面应力还是平面应变,GM准则计算结果与Mises结果均有最佳接近度。     

Distribution of dislocations at a mode I crack tip and their shielding effect

Distribution of dislocations at a finite mode I crack tip is formulated. Closed form solutions for the dislocation distribution function, the dislocation-free zone (DFZ), the local stress intensity factor and the crack tip stress field are obtained. The dislocation distribution has similar features to a mode III crack model. Under a given applied stress, there may exist different configurations of plastic zone and DFZ. Crack tip shielding by dislocations depends on both applied stresses and the configuration.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

Dynamic plastic response of a circular plate based on unified strength theory

The study and design of structures under dynamic loads require a knowledge of the plastic response and deformation behavior under impact loading. The calculations of dynamic plastic response of structures are useful for the design and investigation of colliding vehicle, engine and various impacting structures. The unified solutions of dynamic plastic load-carrying capacities, moment fields and velocity fields of a simply supported circular plate are introduced. The strength is different in tension and compression and the effect on the yield criteria is taken into account by using the unified strength theory. Upper bound and lower bound plastic responses of the plate, under moderate partial uniformly distributed impulsive loading, are obtained. The static and kinematical admissibility of the dynamic plastic solutions are discussed. The unified solutions of the static plastic load-carrying capacities, moment fields and velocity fields of a simply supported circular plate are also obtained according to the dynamic solutions in this paper. The solutions are suitable for many materials with or without different strengths in tension and compression and the effect of intermediate principal stress.The solutions based on the Tresca, the von Mises, the Mohr–Coulomb theory, and the twin-shear strength theory, as well as the unified yield criterion, are all the special cases of the unified solutions. The influences of the coefficient of failure criteria, b, and tension-compression strength ratio, α, on the dynamic and static solutions, are investigated. It is shown that the effects of different strengths in tension and compression and yield criteria on the dynamic load-carrying capacity are greater than in the static plastic limit state.     

Plastic zone correction on a Zener–Stroh crack interacting with a circular inclusion in ductile materials

Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with a circular inclusion (fibre) in fibre‐reinforced composites has been carried out. The Zener–Stroh crack is initiated near the fibre in the pure matrix. Plastic zone correction is introduced the first time for such a crack–inclusion interaction problem so that the fracture behaviour can be analysed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed‐mode problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the inclusion has great effect on the elastic–plastic fracture behaviour of the crack. In our study, the plastic zone size (PZS), crack tip opening displacement (CTOD) and effective stress intensity factor (SIF) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fibre) shear modulus, crack–inclusion distance and the crack sharp tip position on the fracture behaviour of the crack is discussed. It is found that the shear modulus ratio and the crack–inclusion distance have great effect on the normalized values of PZS and CTOD, but the effects highly depend on the crack sharp tip position.     

The effect of T‐stress on crack‐tip plastic zones under mixed‐mode loading conditions

In this paper, the influence of T‐stress on crack‐tip plastic zones under mixed‐mode I and II loading conditions is examined. The crack‐tip stress field is defined in terms of the mixed‐mode stress intensity factors and the T‐stress using William's series expansion. The crack‐tip stress field is incorporated into the Von Mises yield criteria to develop an expression that determines the crack‐tip plastic zone. Using the resultant expression, the plastic zone is plotted for various combinations of mode II to mode I stress intensity factor ratios and levels of T‐stress. The properties of the plastic zone affected by T‐stress and mixed‐mode phase angle are discussed. The observations obtained on plastic zones variations are important for further fatigue and fracture analyses for defects in engineering structures under mixed‐mode loading conditions.     

考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解

平面应变条件下的深埋圆形巷道问题一般忽略中间主应力的影响,但这会与塑性区围岩的实际情况产生较大差异。为了充分考虑中间主应力对深埋圆形巷道的影响,基于平面应变假设与非关联流动法则将Mohr-Coulomb准则精确匹配为Drucker-Prager准则,在此基础上推导了考虑剪胀特性的理想弹塑性材料在塑性阶段的中间主应力表达式,中间主应力与剪胀角密切相关;根据所得的中间主应力表达式结合非关联流动法则,不引入任何假设,得出深埋圆巷塑性区由于剪胀角而发生体变的关系式;进一步推导了考虑中间主应力和剪胀特性的深埋圆形巷道塑性区应力位移解析式,其中径向应力、切向应力及塑性区半径的表达式与卡斯特奈(Kastner)解完全一致,但卡斯特奈(Kastner)解无法得出中间主应力,而新的位移解析式则与以往的文献完全不同;经与以往文献的位移理论解比较分析知,新的位移解答更加合理。因此考虑中间主应力和剪胀特性的解答为深埋圆形巷道的计算与设计提供一定的理论基础。