Numerical analysis of the components of the three-dimensional non-singular stress field at a mixed-type crack tip

A program was developed that allows one to automate the process of calculating the three-dimensional stress field at a mixed-type crack tip within the ANSYS software. The calculation results are given for the stress intensity factors and components of the non-singular T-stress for the disk model with an inclined crack under compression with a varying thickness of the sample and an approximately constant parameter of mixing of the types of stress (I + II). We note the significant influence of the thickness of the sample on the nonsingular T _zz -stress when the value of the T _xx stress changes negligibly.     

Fully plastic analyses of unequally notched specimens in bending

This paper proposes slip line fields for bending of unequally notched specimens in plane strain, that have a sharp crack in one side and a sharp V-notch in the other side. Depending on the back angle, two slip line fields are proposed, from which the limit moment and crack tip stress fields are obtained as a function of the back angle. Excellent agreement between slip line field solutions with those from detailed finite element limit analysis based on non-hardening plasticity provides confidence in the proposed slip line fields. One interesting point is that, for the unequally notched specimen, the difference between the crack tip triaxial stress for tension and that for bending increases significantly with the increase in the back angle. This suggests that such a specimen could be potentially useful to investigate the crack tip constraint effect on fracture toughness of materials. In this respect, the possibility of designing a new toughness testing specimen with varying crack tip constraint is discussed.     

平面应力条件下裂端约束与裂纹启裂准则

本文利用有限元方法对平面应务条件下带有不同裂纹深度的各种裂纹试样裂端应力三轴性约束水平及其他性质进行了大量的计算分析。结果表明：平面应力裂端约束强度完全符合HRR场的要求,而且与试样几何形状、裂纹深度、材料状态等基本无关。由此确保了J积分主导裂端场的有效性、裂纹启裂准则的材料党数性质及其有同等裂端约束条件下表征不同材料断裂韧度的可比性,并得到实验结果的证明。     

不同裂纹深度裂端约束强度与启裂准则

对50D钢三点弯曲试样的有限元分析与实验结果表明：不同裂纹深度试样裂端应力三轴性各异且不能满足HRR场约束强度要求是造成J主导失效及启裂J I随裂纹深度变化,不是材料常数的本质原因。提出了一个新型弹塑性启裂准则,并利用现有的实验结果证明J (vi)是与裂纹深度无关的材料常数。     

Moving finite element analyses for fast crack propagation in sheet metal

The conventional fracture mechanics parameters K_IC and/or J_IC are used as fracture toughness criteria necessary for the start of crack propagation under plane strain conditions. These criteria are defined only for small-scale yielding or infinitesimal deformation, though actual fractures involve large plastic deformation. Hence, measurement of fracture resistance during crack propagation is difficult with the conventional parameters.Estimating the mechanical conditions around the propagating crack tip is very useful for reducing damage during accidental fracture. Therefore, establishing a criterion for crack propagation with large-scale yielding is very important for not only science fields but also some industrial fields. For fractures with large-scale yielding, micro- or mesoscale damage processes in the crack tip vicinity have to be considered.In this study, Gurson's constitutive model for void occurrence and growth was introduced into the finite element method to discuss failure behavior in the crack tip vicinity. Fast crack propagation behavior under high-speed deformation was simulated using the moving finite element method based on the Delaunay automatic triangulation. The excellent far-field integral path independence of the T* integral was verified for pure mode I fast crack propagation and non-straight crack propagation under mixed mode conditions. The void growth conditions near the crack propagation path were evaluated.     

Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios (a/c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J–Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances (r/(J/σ₀)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/σ₀) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ_e, the hydrostatic stress σ_m and the stress triaxiality R_σ, the three-parameter J–Q_T–T_z approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor T_z and the Q_T term, which is determined by matching the finite element analysis results, the J–Q_T–T_z solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/c and n. Finally, the empirical formula of T_z and the stress components are provided to predict the stress state parameters effectively.     

The plane-strain general yielding of notched members due to combined axial force and bending—II: Deep circular notches

The slip-line fields proposed by Green for the plane-strain general yielding of notched plates in pure bending are generalized to provide solutions for notched plates subjected to combined axial force and bending. Deep symmetrical circular notches and single circular notches are considered. For notched plates subjected to arbitrary combinations of axial force and bending, two constraint factors are obtained, T₁ due to the axial force and M₁ due to the bending moment. These constraint factors are shown to have characteristic relationships on the T₁−M₁ plane for the single notched plate and the symmetrically notched plate. The derivations of these general yielding loci are described in detail and the statical and kinematical limitations of the slip-line fields are discussed. Finally it is demonstrated that the corresponding strain-rate vectors are normal to these loci and that, therefore, these loci can be regarded as plastic potentials.     

Effect of high-pressure rheology of lubricating oils on boundary lubrication

High-pressure rheology of lubricating oil was determined using different experiments, and the phase diagram was drawn. The four-ball wear tests were used to evaluate anti-wear characteristics of oils in boundary lubrication condition. The bridged ring compound oils showed the minimum wear scar in the four-ball wear tests. The diameter of wear scar decreases with increasing the elastohydrodynamic film-forming capability. Next, we considered the molecular packing parameter T_VE−T at the four-ball wear test. The T_VE−T values of bridged ring compound oils were in the range 250-360 and oils were elastic-plastic solid. It is concluded that the solidified oil film under boundary lubrication conditions has the anti-wear action.     

Dynamic mixed mode crack propagation behavior of structural bonded joints

The stress field around the dynamically propagating interface crack tip under a remote mixed mode loading condition has been studied with the aid of dynamic photoelastic method. The variation of stress field around the dynamic interface crack tip is photographed by using the Cranz-Shardin type camera having 10⁶ fps rate. The dynamically propagating crack velocities and the shapes of isochromatic fringe loops are characterized for varying mixed load conditions in double cantilever beam (DCB) specimens. The dynamic interface crack tip complex stress intensity factors,K ₁ andK ₂, determined by a hybrid-experimental method are found to increase as the load mixture ratio of y/x (vertical/horizontal) values. Furthermore, it is found that the dynamically propagating interface crack velocities are highly dependent upon the varying mixed mode loading conditions and that the velocities are significantly small compared to those under the mode I impact loading conditions obtained by Shukla (Singh & Shukla, 1996a, b) and Rosakis (Rosakis et al., 1998) in the USA.     

环氧树脂的增韧对裂尖约束的影响

对用不同增韧方法制成的环氧树脂材料进行了断裂性能分析,结合有限元计算,得到了裂尖约束以及不同增韧方法对裂尖应力应变场的影响。同时,给出了裂尖钝化半径与裂纹尖端应力应变场的关系,指出：在一定的载荷水平下,可以有效地降低裂纹尖端的应力水平,降低裂纹尖端的三轴应力度,提高结构的承载水平。本文还指出增韧有利于提高材料的断裂性能,降低裂纹尖端的三轴应力度。     

Experimental and numerical study on the burst pressure of steam generator tubes with L- and U-type through-wall combination cracks

Several nuclear power plants have reported that they often experience through-wall combination cracks consisting of longitudinal and circumferential cracks in the steam generator tubes. In this study, L- and U-type through-wall combination cracks in a steam generator tube were evaluated using the crack opening angle (COA) in an elastic-plastic analysis. The calculated burst pressures were also compared with the experimental results. In the procedure, the stress intensity factor (K _I) in elastic analysis was reviewed to validate COA as an appropriate fracture parameter for the burst pressure of longitudinal through-wall cracks and T-type through-wall combination cracks. From the results, an appropriate length-based burst criterion by using COA can be used for a structural integrity assessment for the through-wall combination cracks in steam generator tubes.     

The effect of deformation anisotropy on the plastic zone at the tip of a crack under biaxial loading

A theoretical analysis for investigating the form and dimension of the plastic zone in the tip of a crack in a plate made from a material with deformation anisotropy is presented. The anisotropy is explained by the hardening process during plastic deformation caused by loading along a straight-line trajectory until a crack is formed in the plate plane. The idea of this method is to take into account the second term in the Williams’ series representation in eigenfunctions for stress components for the 2D case. The contribution of the second term in the Cartesian coordinate system is independent of the distance from the crack tip for the K ₁ − T concept. It is shown that for the case of anisotropy, the dimension of the plastic zone decreases. The stress along the crack’s axis changes the plastic zone significantly.     

The plane-strain general yielding of notched members due to combined axial force and bending—I: Wedge-shaped notches with large flank angles

The slip-line field proposed by Green for the general yielding of notched plates in pure bending is generalized to provide solutions for the general yielding of notched plates subjected to combined bending and axial force. For symmetrically notched plates subjected to arbitrary combinations of axial force and bending moment, two constraint factors are obtained, T₁ due to the axial force and M₁ due to the bending moment. These constraint factors are shown to have a characteristic locus expressed by two parabolae in the T₁ − M₁ plane. In one extreme case where both flank angles are equal to π, i.e. a flat plate, the locus is the same as that obtained by Prager.The general yielding loci of single notched plates and plates containing symmetrical notches of the same flank angle are derived as special cases of the general problem and some practical problems involving single notches are considered.     

The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface

For the fracture evaluation of inclined cracks terminating at the dissimilar material interface, not only the singularities, but also the detailed stress field and its stress intensity factors are necessary. However, though there are many researches reported on the singularity analysis, the stress field and its stress intensity factors are still not clear. This paper has deduced theoretically the singular stress and displacement fields near the tip of a crack terminating at the interface between bonded dissimilar materials, for both cases of real and oscillatory singularities. From the deduced singular stress field, the stress intensity factors are defined for such a crack, and the corresponding numerical extrapolation methods are also proposed. Through the numerical examinations, it is found that the theoretical stress distributions agree well with the numerical results obtained by the finite element method. Moreover, the proposed extrapolation method shows a good linearity, thus it can be used as an efficient way to determine the characteristics of the stress and displacement fields near the tip of a crack terminating at interface.     

The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading

The goal of this paper is to provide the foundation for an analysis of contact between elastic-plastic solids, whose surface roughness is idealized with a Weierstrass profile. To this end, we conduct a parametric study of the plastic deformation and residual stress developed by the two-dimensional contact between a flat, rigid platen and an elastic-perfectly plastic solid with a sinusoidal surface. Our analysis shows that the general characteristics of the deformation can be characterized approximately by two parameters: α = a/λ, where a is the half-width of the contact and λ is the period of the surface waviness; ψ = E^*g/σ_Yλ, where E^* and σ_Y are the effective modulus and yield stress of the substrate, respectively, and g is the amplitude of the surface roughness. Depending on the values of these parameters, we identify eight general types of behavior for the asperity contacts: (a) elastic, elastic-plastic or fully plastic isolated Hertz type contacts; (b) elastic, or elastic-plastic non-Hertzian isolated contacts; and (c) elastic, elastic-plastic or fully plastic, interacting contacts. Relationships between contact pressure, contact size, effective indentation depth and residual stress are explored in detail in each regime of behavior. Implications on rough surface contacts are discussed.     

裂纹端约束效应与18G2A钢JR曲线可转移性

采用有限元和J—A2方法对18G2A钢进行弹塑性断裂分析。通过引入一修正因子使J—A2的控制区进一步扩大，得到的结果与有限元分析结果相当吻合。在计算各单边缺口弯曲试件裂纹端的应力场后，得到了不同深浅裂纹的约束参数A2。同时，为了将实验得到的18G2A钢的JR曲线应用于实际裂纹构件，建立了JR曲线与约束参数A2之间的关系，给出了与约束参数A2相关的JR曲线族的表达式。由此预测的JR曲线与实验数据吻合较好，具有较好的工程应用价值。     

Mode I fracture toughness analysis of a single-layer grapheme sheet

To predict the fracture toughness of a single-layer graphene sheet (SLGS), analytical formulations were devised for the hexagonal honeycomb lattice using a linkage equivalent discrete frame structure. Broken bonds were identified by a sharp increase in the position of the atoms. As crack propagation progressed, the crack tip position and crack path were updated from broken bonds in the molecular dynamics (MD) model. At each step in the simulation, the atomic model was centered on the crack tip to adaptively follow its path. A new formula was derived analytically from the deformation and bending mechanism of solid-state carbon-carbon bonds so as to describe the mode I fracture of SLGS. The fracture toughness of single-layer graphene is governed by a competition between bond breaking and bond rotation at a crack tip. K-field based displacements were applied on the boundary of the micromechanical model, and FEM results were obtained and compared with theoretical findings. The critical stress intensity factor for a graphene sheet was found to be K _IC = 2.63 ~ 3.2MPa \(\sqrt m \) for the case of a zigzag crack.     

Modified boundary layer analysis for a mode III crack problem

A modified boundary layer problem of a semi-infinite crack in an elastic-perfectly plastic material under a Mode III load is analyzed. The analytic solution of elastic fields is derived by using complex function theory. It is found that the size and the shape of the plastic zone near the crack tip depend on the elastic T-stress given on the remote boundary. A method for determining higher order singular solutions of elastic fields is also proposed. In order to determine the higher order singular solutions of the elastic fields, Williams expansion of the solution is used. Higher order terms in the Williams expansion are obtained through simple mathematical manipulation. The coefficients of each term in the Williams expansion are also calculated numerically with the J-based mutual integral     

Field evaporation behavior in [0 0 1] FePt thin films

Though the atom probe has provided unprecedented atomic identification and spatial imaging capability, the basic reconstruction assumption of a smooth hemispherical tip shape creates significant challenges in yielding high fidelity chemical information for atomic species with extreme differences in fields required for field evaporation. In the present study, the evaporation behavior and accompanying artifacts are examined for the super-cell lattice structure of L1₀ FePt, where alternating Fe and Pt planes exist in the [0 0 1] orientation. Elemental Fe and Pt have significant differences in field strengths providing a candidate system to quantify these issues. Though alloys can result in changes in the elemental field strength, the intrinsic nature of elemental planes in [0 0 1] L1₀ provides a system to determine to what extent basic assumptions of elemental field strengths can break down in understanding reconstruction artifacts in this intermetallic alloy. The reconstruction of field evaporation experiments has shown depletion of Fe at the (0 0 2) pole and zone axes. Compositional profiles revealed an increase in Fe and atom count moving outward from the pole. The depletion at the low indexed pole and zone axes was determined to be the result of local magnification and electrostatic effects. The experimental results are compared to an electrostatic simulation model.     

Characteristics of a transiently propagating crack in functionally graded materials

When a crack propagates with acceleration, deceleration and time rates of change of stress intensity factors, it is very important for us to understand the effects of acceleration, deceleration and time rates of change of stress intensity factors on the individual stresses and displacements at the crack tip. Therefore, the crack tip stress and displacement fields for a transiently propagating crack along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density are developed and the characteristics of a transiently propagating crack from the fields are analyzed. The effects of the rate of change of the stress intensity factor and the crack tip acceleration on the individual stresses at the crack tip are opposite each other. Specially, the isochromatics (constant maximum shear stress) of Mode I tilt backward around the crack tip with an increase of crack tip acceleration, and tilt forward around the crack tip with an increase of the rate of change of the dynamic mode I stress intensity factor. This paper was recommended for publication in revised form by Associate Editor Chongdu Cho Kwang-Ho Lee received a Ph.D. degree in Yeungnam University in 1993. Dr. Lee is currently a professor at the School of Mechanical and Automotive Engineering at Kyungpook National University in Korea. He also had worked in KOMSCO as an engineer and researcher (1982.3–1996.2). He is interested in the fields of fracture and stress analysis on the composite, interface, nano and functionally graded materials by theoretical and experimental mechanics. Specially, his major interest is analysis of dynamic crack tip fields. Young-Jae Lee received his B.S degree in Agricultural Civil Engineering from Gyeongsang National University (GNU) in 1982. He then received his M.S. and Ph.D. degrees from GNU in 1984 and 1995, respectively. Dr. Lee is currently a professor at the department of Civil Engineering at Kyungpook National University in Korea. From 2005 to 2006, he had served as an editor of Korea Institute for Structure Maintenance and Inspection. His research interests are in the area of evaluation, diagnosis and optimum design of structure. Sang-Bong Cho received a Ph. D. degree from Tokyo University in 1989. Dr. Cho is currently a professor at the division of Mechanical and Automation Engineering at Kyungnam University in Korea. His research interests are in the area of fracture mechanics, FEM stress analysis and fretting fatigue.