有限厚度板穿透裂纹前缘附近三维弹性应力场分析

通过三维有限元计算来研究有限宽度、有限厚度含有穿透裂纹板的裂纹前缘应力场，从中找出应力强度因子与板的厚度、裂纹长度之间的关系，同时还分析了裂尖的三维约束程度和三维约束区的大小。分析结果表明：应力强度因子沿厚度的分布是不均匀的，应力强度因子的最大值及其位置与厚度有关；有限厚度板中面应力强度因子(KI)m-p及最大应力强度因子(KI)max均大于平面应力或平面应变的应力强度因子。对有限厚度裂纹问题，按平面应力或平面应变来考虑是不安全的；板中面的应力强度因子(KI)m-p及最大应力强度因子(KI)max是厚度B／a的函数；板的中面离面约束系数Tx最大，自由面(z=B)Tx=0。沿厚度方向裂尖附近的离面约束系数Tx也是z／B和B／a的函数，随着厚度的增加离面约束系数Tx增大，离中面越近离面约束系数Tx越大。Tx随着x的增大急剧减小，三维约束影响区域大小大约为板厚的一半，且裂纹长度a／W对应力强度因子沿厚度变化规律及Tx影响区域大小影响较小。     

CONSTRAINTS ON THE CRACK TIP PLASTIC FIELDS UNDER LARGE SCALE YIELD

Plane strain elastic-plastic finite element analyses are used to study the stress, strain fields around a straight crack in power hardening plastic material. Center crack panel (CCP), single edge crack panel (SECP) and double edge crack panel (DECP) tension specimens are analyzed with various crack lengths. Two local constraint parameters, i.e. in-plane stress ratioT _x and out-of-plane constraintT are analyzed, which are defined as tangential stress dividing normal (open) stress and out-of-plane stress dividing the sum of tangential stress and normal stress respectively. Numerical analyses indicate that the two local constraint parameters are nearly independent of the specimen geometry and the loading level in the plastic zone. Methods of estimating two constraint parameters and ways to define the boundary of the blunt zone are given. By using these parameters, the stress distributions in the plastic zone, especially in the blunt zone can be accurately predicted. Project supported by the National Foundation of Distinguished Young Scientists of China (No. 59625510).     

Characterization of crack tip stresses in plane-strain fracture specimens having weld center crack

Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (I_p) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK _I , the crack tip biaxiality parameter is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK _I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK _I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.     

侧槽的拘束作用及对断裂韧性参量的影响

本文研究了侧槽对预制疲劳裂纹Ｃｈａｒｐｙ尺寸试样的拘束效应以及其对断裂韧性参量的影响。当侧槽深度大于临界值时，峰值载荷韧性Ｊｍ值与起裂韧性Ｊ１值基本相等。侧槽对试样的加厚作用可用试样的附加厚度表示，对于同样的侧槽深度，不同材料具有不等的附加厚度，试样取得最大附加厚度的侧槽深度为３３％。文中提出用拘束系数定量地估计侧槽对裂纹尖端的塑性拘束作用，能较好地解解放本试验结果。     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

Mode II stress intensity factors for a crack parallel to the surface of an elastic half-space subjected to a moving point load

The direction of propagation of rolling contact fatigue cracks is observed to depend upon the direction of motion of the load. In this paper approximate calculations are described of the variation of Mode II stress intensity factors at each tip of a subsurface crack, which lies parallel to the surface of an elastic half-space, due to a load moving over the surface. In particular the effect of frictional locking of the crack faces under the load is investigated. In consequence of frictional locking the range of SIF at the trailing tip ΔK_T is found to be about 30% greater than that of the leading tip ΔK_L, which is consistent with observations that subsurface cracks propagate predominantly in the direction of motion of the load over the surface. The effects on k_t and k_lof crack length, crack face friction, traction forces at the surface and residual shear stresses are also investigated.     

Role of elasticity in elastic–plastic fracture: Analytical bi-linear crack-tip fields and finite element analysis

A solution for Model-I plane strain crack tip fields in a bi-linear elastic–plastic material is presented. The elastic–plastic Poisson's ratio is introduced to characterize the influence of elastic deformation on the near tip constraint. Attention is focused on the distribution of elastic/plastic strain energy in the sensitive region of the forward sector ahead of a crack tip. The present study shows that the elastic strain energy can be higher than the plastic strain energy in this sensitive sector while large amount of the plastic strain energy develops outside this sector around the crack tip. The effect of elastic deformation in this sensitive region on the structure of crack-tip fields is considerable and the assumption in some important solutions for crack-tip fields reported in literature that the elastic deformation is small and can be ignored is therefore not physically reasonable. Besides, finite element analysis is carried out to validate the analytical solution and good agreement between them is found. It is seen that the present solution with T-stress can properly describe the crack-tip fields under various constraints for different specimens and an analytical relation is established between the critical value of J-integral, J_c, and T-stress for elastic–plastic fracture.     

裂尖大变形条件下的约束研究

通过面内应力比Tx和离面约束Tz在塑性区分布规律的深入分析，发现约束在塑性区不同区域的影响是不同的，在裂尖的钝化区，面内应力比Tx起重要作用，而在钝化区外的塑性区内，离面约束Tz起主要作用，在J－Q理论的基础上引入离面约束Tz可以很好地描述钝化区以外的应力应变分布，在钝化区内引入面内应力比Tx可以对裂尖前方的应力应变进行大变形分析和描述，研究表明综合两个约束的共同作用，可以很好地描述大变形条件下裂尖前方的应力分布。     

Equivalent thickness conception for corner cracks

Thickness dependence of the one-parameter-based fracture toughness has been well recognized and widely studied. However, it is still a challenge to predict the fracture of structures with curved cracks from the fracture toughness data obtained from the standard through-the-thickness cracked specimens. The complicated three-dimensional (3D) stress fields near the crack front play a vital role in the fracture strength of materials. Based on a systematical numerical study of the 3D stress fields near the crack tip of quarter elliptic corner cracks and comparison with that of ideal through-the-thickness cracks, an equivalent thickness conception for curved cracks is proposed from the viewpoint of out-of-plane constraint, and a semi-analytical solution for the equivalent thickness of corner cracks is obtained. With the evaluated equivalent thickness, the fracture toughness of corner cracked specimens is predicted efficiently by the plane-strain toughness value of the material obtained from the standard through-the-thickness specimen.     

Stress intensities for nozzle cracks in reactor vessels

A series of six frozen stress photoelastic tests was conducted to investigate the distribution of stress-intensity factor (SIF) along a crack which occurred at the juncture of a pipe (nozzle) with a cylindrical pressure vessel. Typical photoelastic-fringe patterns are shown for slices which were taken mutually orthogonal to the flaw border and the flaw surface. A typical plot of normalized apparent SIF vs. square root of normalized distance from the crack tip is presented. The variation in SIF along the flaw border is given for all six different crack geometries and, also, the variation of SIF with varyinga/T is presented.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper, three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip. of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program. The results reveal that the constraints along the thickness direction are obviously separated into two parts: the keeping similar high constraint field (Z₁) and rapid reducing constraints one (Z₂). The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively. So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively. The distribution of the Crack Tip Opening Displacement (CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio (V_g) near the crack tip are also obtained. The two fracture parameters are in similar trends along the thickness direction, and both of them can reflect the effect of thickness and that of the loading level to a certain degree.     

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

The generalized Dugdale crack model is used to formulate two-parameter failure criteria for the cases of quasibrittle state and developed plastic zones at a mode I crack tip. The failure criteria relate the fracture strength characteristics and the stress mode at the crack tip through the plastic constraint factor. The critical state of bodies with cracks under uni-and biaxial loading is analyzed in the cases of plane stress and plane strain using the Tresca and von Mises yield criteria. A small-scale yield criterion, which is an analytic relation between the critical stress intensity factor and T-stresses, is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 47–57, July 2007.     

A Peierls criterion for the onset of deformation twinning at a crack tip

A criterion for the onset of deformation twinning (DT) is derived within the Peierls framework for dislocation emission from a crack tip due to Rice (J. Mech. Phys. Solids 40(2) (1992) 239). The critical stress intensity factor (SIF) is obtained for nucleation of a two-layer microtwin, which is taken to be a precursor to DT. The nucleation of the microtwin is controlled by the unstable twinning energyγ_ut, a new material parameter identified in the analysis. γ_ut plays the same role for DT as γ_us, the unstable stacking energy introduced by Rice, plays for dislocation emission. The competition between dislocation emission and DT at the crack tip is quantified by the twinning tendencyT defined as the ratio of the critical SIFs for dislocation nucleation and microtwin formation. DT is predicted when T>1 and dislocation emission when T<1. For the case where the external loading is proportional to a single load parameter, T is proportional to . The predictions of the criterion are compared with atomistic simulations for aluminum of Hai and Tadmor (Acta Mater. 51 (2003) 117) for a number of different crack configurations and loading modes. The criterion is found to be qualitatively exact for all cases, predicting the correct deformation mode and activated slip system. Quantitatively, the accuracy of the predicted nucleation loads varies from 5% to 56%. The sources of error are known and may be reduced by appropriate extensions to the model.     

高温结构蠕变裂尖拘束效应

如何对蠕变裂纹扩展寿命进行准确预测和评价是高温结构完整性评定、寿命设计和运行维护中需要解决的核心问题.基于宏观单参数C?的蠕变断裂行为的评价方法,未有效纳入裂尖拘束效应的影响,因而其评价结果过于保守或非保守.目前国内外还未建立起有效纳入裂尖拘束效应的高温结构蠕变寿命评价的理论体系和技术方法,还没有纳入蠕变拘束效应的高温结构完整性评定规范.本文综述了作者近年来在高温蠕变断裂拘束效应方面的研究工作.主要包括:裂尖拘束对材料蠕变裂纹扩展行为的影响及机理;蠕变裂尖场和拘束参数R的定义和影响因素;载荷无关的蠕变拘束参数R? 的提出及其应用基础;承压管道表面裂纹的拘束参数R? 解及纳入裂尖拘束的蠕变寿命评价方法;试样与管道轴向裂纹蠕变裂尖拘束的关联;基于裂尖等效蠕变应变的面内与面外蠕变裂尖拘束的统一表征参数Ac的研究;材料拘束相关的蠕变裂纹扩展速率的建立;宽范围C? 区蠕变裂纹扩展速率及其拘束效应的数值预测;材料拘束对焊接接头蠕变裂纹扩展行为的影响及机理等.这些研究为建立纳入裂尖拘束效应的高温部件的蠕变裂纹扩展寿命评价方法奠定了理论和技术基础.论文对后续拟开展的工作也进行了展望.     

Effect of intrinsic stress gradient on the effective mode-I fracture toughness of amorphous diamond-like carbon films for MEMS

The influence of intrinsic stress gradient on the mode-I fracture of thin films with various thicknesses fabricated for Microelectromechanical Systems (MEMS) was investigated. The material system employed in this study was hydrogen-free tetrahedral amorphous diamond-like carbon (ta-C). Uniform gauge microscale specimens with thicknesses 0.5, 1, 2.2, and 3 μm, containing mathematically sharp edge pre-cracks were tested under mode-I loading in fixed grip configuration. The effective opening mode fracture toughness, as calculated from boundary force measurements, was 4.25±0.7 MPa√m for 0.5-μm thick specimens, 4.4±0.4 MPa√m for 1-μm specimens, 3.74±0.3 MPa√m for 2.2-μm specimens, and 3.06±0.17 MPa√m for 3-μm specimens. Thus, the apparent fracture toughness decreased with increasing film thickness. Local elastic property measurements showed no substantial change as a function of film thickness, which provided evidence for the stability of the sp²/sp³ carbon binding stoichiometry in films of different thicknesses. Detailed experiments and finite element analysis pointed out that the dependence of the effective fracture toughness on specimen thickness was due to the intrinsic stress gradient developed during fabrication and post-process annealing. This stress gradient is usually unaccounted for in mode-I fracture experiments with thin films. Thicker films, fabricated from multiple thin layers, underwent annealing for extended times, which resulted in a stress gradient across their thickness. This stress gradient caused an out-of-plane curvature upon film release from its substrate and, thus, combined bending and tensile mode-I loading at the crack tip under in-plane forces. Since the bending component cannot be isolated from the applied boundary force measurements, its contribution, becoming important for thick films, remains unaccounted for in the calculation of the critical stress intensity factor, thus resulting in reduced apparent fracture toughness that varies with film thickness and curvature. It was concluded that in the presence of a stress gradient, accounting only for the average intrinsic stresses could lead in an overestimate of the fracture resistance of a brittle film. Under these considerations the material fracture toughness of ta-C, as determined from specimens with negligible curvature, is K_IC=4.4±0.4 MPa√m.