On the fundamental basis of fracture mechanics

Based on the crack tip stress and strain fields, the linear and the non-linear fracture mechanics have been developed. Their applications to the studies of fracture initiation and stable crack growth may differ because of the difference in the basic postulates of various fracture theories. The correct postulates will help to develop non-linear fracture mechanics for valid fracture toughness measurements and to extend fracture mechanics beyond the realms of K and J.The basic postulates of the linear elastic fracture mechanics are examined. The theory of global energy balance, the theory of sharp notch, and the theory of the characterization of crack tip stress and strain fields by K are analyzed. Fracture initiation and stable crack growth are local fracture phenomena. Therefore the global energy balance theory for crack initiation and stable crack growth without the study of the detailed fracture processes is fortuitous. The capability of the stress intensity factor to characterize the crack tip stress and strain fields for the localized fracture process is the basis for the validity of the linear elastic fracture mechanics.The concept of the characteristic crack tip field can be directly extended to the non-linear fracture mechanics. The fracture toughness and the tearing modulus of a tough material are measures of the fracture ductility of the material. The possibility to extend fracture mechanics beyond the realms of K and J are discussed.     

Failure analysis of a cracked plate based on endochronic plastic theory coupled with damage

An anisotropic model of damage mechanics for ductile fracture incorporating the endochronic theory of plasticity is presented in order to take into account material deterioration during plastic deformation. An alternative form of endochronic (internal time) theory which is actually an elasto-plastic damage theory with isotropic-nonlinear kinematic hardening is developed for ease of numerical computation. Based on this new damage model, a finite element algorithm is formulated and then employed to characterize the fracture of thin aluminum plate containing a center crack. A new criterion termed as Y _R-Criterion is proposed to define both the crack initiation angle and load. Experiments have been conducted to verify the validity of the proposed damage model and it is found that the theoretical crack initiation loads correspond closely with the measured values.     

A failure criterion for brittle and quasi-brittle materials under any level of stress concentration

In this paper, we present a new criterion to predict the crack initiation under quasi-static loads from a geometrical weakness presenting an arbitrary stress concentration in brittle or quasi-brittle materials. Three material parameters were used in the establishment of the criterion, namely the ultimate stress σ_c, the critical energy release rate for crack growth G_c and the critical energy release rate for fracture under uniform uniaxial tension G_u. The use of these two critical energy release rates was justified by the observation of the fracture surfaces under different stress concentrations. The proposed three parameters’ concept enables to take the different stress concentration levels into account, thus provides a unified criterion to predict crack initiation for any stress concentration, whatever it is singular or regular. Numerous experimental studies were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.     

Fracture initiation under gross yielding: Strain energy density criterion

The damage of metal alloys at the continuum level can be described by a combined process of yielding and fracture. Yielding is generally associated with excessive distortion and fracture with excessive dilatation. With the increased use of low strength alloys, gross yielding can often precede the initiation of macrocracking. This paper applies the strain energy density concept for examining failure by crack growth in a fully plastic material in order to show that the criterion applies to linear elastic as well as nonlinear plastic materials. The incremental theory of plasticity is employed in conjunction with the finite element method for determining the stresses in a tensile specimen containing a center crack. Net section yield is developed. Calculated are the different levels of intensity of yielding around the crack. As in the elastic case, crack growth in a fully plastic material also tends to coincide with the direction along which the strain energy density function dW/dV attains a relative minimum. The onset of crack growth is assumed to occur when (dW/dV)_min reaches some critical value $\text{(d W/d V)}{}_{\mathrm{c}}{}^1$ which must now be obtained from the true stress and strain curve of the material undergoing gross yielding.     

A fatigue reliability analysis method including super long life regime

An affordable and feasible method with moderate accuracy is developed to realize fatigue reliability assessment and life prediction including super long life regime (SLLR) through series of experimental researches on a railway axle steel and real axles. A competition damage mechanism for fatigue crack initiation and growth in SLLR is revealed to fascinate an understanding on wide fatigue damage behavior and to provide a weigh and balance on material primary quality control and on-line inspection capacity. Affordable material probabilistic strength-life (S-N) curves including SLLR are presented by an extrapolation approach on a concurrent probability rule between the S-N relations in mid-long life regime and the fatigue limits with a specified life definition. And then, structural probabilistic S-N curves are deduced by considering scale-induced effect on the material curves. Random cyclic stress-strain (CSS) relations are depicted for constructing structural random stressing history. Reliability assessment and fatigue life prediction are conducted by an interference model of the applied stress deduced from the random CSS relations and the strength capacity derived from the structural probabilistic S-N curves. Availability and feasibility of the present method are indicated by a successful application on a railway axle steel.     

Effect of interface layer consisting of nanosprings on stress field near interface edge

The purpose of this study is to investigate the effect of an interface layer consisting of discretely arrayed nano-sized elements on stress intensified fields. A material where an interface layer consisting of Ta₂O₅ helical nanoelements (nanosprings) is inserted between dissimilar components is prepared and two types of crack initiation experiments, which possess radically different stress conditions, are carried out. The finite element analyses indicate that the stress fields in the components with and without the interface layer are completely different, and it is experimentally clarified that the fracture mechanics concept cannot be applied to the crack initiation at the dissimilar interface edge with the interface layer. The stress distributions at the crack initiation reveal that the crack initiation is governed by the apparent stress of the nanospring, σ′, at the edge. This signifies that the interface layer eliminates the stress singular field at the interface edge. The criterion of the crack initiation is evaluated as .     

On the influence of state of stress on ductile failure initiation in high strength steels

The effect of stress state on the effective plastic strain to initiate ductile failure in three high strength steels is investigated. Circumferentially notched tension specimens were used, and failure initiation strains were correlated with a parameter which is a measure of the “triaxiality” of the stress state. Results are given for both in-plane and through-thickness directions in rolled plate.The failure initiation data, together with appropriate stress-strain fields, and estimates of characteristic lengths over which failure initiates, have been used to predict failure initiation at notches and at crack tips; conventional fracture mechanics parameters, such as K_I at crack extension in small scale yielding are estimated for one of the high strength steels.     

结构钢开裂准则及断裂试验分析

为探寻结构钢开裂机理及抗断设防,给出了结构钢在应力三轴空间的广义屈服轨迹方程。结合古典强度理论和现代损伤力学对金属屈服和断裂解释的力学原理,基于三向等拉伸应力状态下结构钢屈服和宏观脆断重合性假设,导出了结构钢在应力三轴空间的开裂准则。在结构钢开孔板的单向等速拉伸断裂试验中,较为精确地测量了初始开裂时的加载位移及全程载荷-位移曲线。试验结果显示,初始裂纹位于孔边且扩展迅速。通过对结构钢开孔板断裂试验的数值模拟分析,对比验证了该开裂准则的普适性及精度。最后,给出了结构钢广义屈服和开裂模型的物理解释及抗断设防。     

A discrete constitutive model for transverse and shear damage of symmetric laminates with arbitrary stacking sequence

A damage constitutive model in conjunction with a 2-D finite element discretization is presented for predicting onset and evolution of matrix cracking and subsequent stiffness reduction of symmetric composite laminates with arbitrary stacking sequence subjected to membrane loads. The formulation uses laminae crack densities as the only state variables, with crack growth driven by both mechanical stress and residual stress due to thermal expansion. The formulation is based on fracture mechanics in terms of basic materials properties, lamina moduli, and critical strain energy release rates G_IC and G_IIC, only. No additional adjustable parameters are needed to predict the damage evolution. Spurious strain localization and mesh size dependence are intrinsically absent in this formulation. Thus, there is no need to define a characteristic length. Comparison of model results to experimental data is presented for various laminate stacking sequences. Prediction of crack initiation, evolution, and stiffness degradation compare very well to experimental data.     

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.     

The reliability of the fracture mechanics approach to environmentally assisted cracking: 1. Uniqueness of the v(K)-curve

This paper analyzes the reliability of the fracture mechanics approach to environmentally assisted cracking in engineering design. A wide collection of experimental evidences of uncertainty in the fracture mechanics characteristics of the phenomenon—the crack growth kinetics v(K)-curve and the threshold stress intensity factor K_th — is presented. Although these basic fracture mechanics items are supposed to depend solely on the material and the environment, they are notably sensitive to the influence of a wide family of test/service variables, producing loss of confidence in materials evaluation and structural integrity assessment.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

The transition between stress corrosion crack growth and plastic fracture

The paper focuses on the behaviour of materials for which the onset of crack extension and unstable fracture coincide in a rising load fracture mechanics test. A theoretical analysis shows that use of the experimental test J_Ic value gives a non-conservative prediction of unstable fracture when a stress corrosion crack grows in a solid that is subject to a sustained high stress. Consequently, when an engineering component is to be used at high stress levels in an environment where stress corrosion cracking might be expected, there are clear advantages in having a material which exhibits stable crack growth in a fracture mechanics test.     

Experimental study of the effect of loading condition on fracture surface contact features and crack closure behavior in a carbon steel

To better understand the crack closure effect in the fatigue process, influence of fatigue stress amplitude and R ratio on the contact features of fracture surfaces in an annealed carbon steel was studied via two special experimental approaches: (i) the collection of the fracture debris fallen from the crack surfaces, and (ii) the direct observation of the contact zones on the fracture surface through an ink dyeing method. The results of this study show that the change of fatigue CMOD value as a function of a/W ratio depends strongly on the loading condition; the fatigue stress amplitude and R ratio are the major factors that determine the contacting status between the mating fracture surfaces; the severity of the fracture surface contact can also be characterized by the dropping rate of the fracture debris particles collected during the fatigue test.     

Micromechanical analysis of mechanical heterogeneity effect on the ductile tearing of weldments

The objective of this study is determination of the effect of mechanical heterogeneity on ductile crack initiation and propagation in weldments using micromechanical approach. Welded single-edge notched bend (SENB) specimens were experimentally and numerically analysed. Material properties of welded joint zones were estimated using a combined experimental and numerical procedure; strains on a smooth tensile specimen were determined using ARAMIS stereometric measuring system in order to obtain true stress – true strain curves. High-strength low-alloyed steel was used as base metal, in quenched and tempered condition. J–R curves and crack growth initiation values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in the heat-affected zone (HAZ) and weld metal (WM). The complete Gurson model (CGM) was used in prediction of J–R curves and crack growth initiation. It is shown that the resistance to crack initiation and growth can be predicted using micromechanical analysis, and that the results are significantly affected by mechanical heterogeneity of the weldment.     

Dominant stress region for crack initiation at interface edge of microdot on a substrate

In order to examine the mechanics of crack initiation at the free interface edge of a microcomponent on a substrate, delamination tests are carried out for two specimen shapes of Cr microdots on a SiO₂ substrate. The microdots of the first specimen are shaped like the frustum of a round cone. The Cr microdots are successfully delaminated from the SiO₂ substrate in a brittle manner and the critical load is measured by atomic force microscopy (AFM) with a lateral loading apparatus. Stress analysis reveals that a singular stress field exists near the interface edge and the strength for the crack initiation is governed by the intensified normal stress field. The critical stress intensity parameter is evaluated as K_σC ≈ 0.24 MPa m^0.39. Similar delamination tests are conducted for microdots shaped like the frustum of an oval cone. The stress distributions at the crack initiation of this specimen shape show a higher normal stress than the first specimen shape in the region near the interface edge of about x < 40 nm, while it is lower in the region of about x > 50 nm (x: distance from the edge). This suggests a limitation of conventional fracture mechanics: namely, the crack initiation in these specimens is not uniquely governed by the intensity of the singular field. It is found that the delamination crack is initiated when the averaged stress σ_ya in the region of 90-130 nm reaches 190-270 MPa, regardless of the specimen shape. This indicates that the dominant stress region of crack initiation is roughly estimated as 90-130 nm and the criterion is given in terms of the averaged stress in the region.     

Anwendung des instrumentierten Kerbschlagbiegeversuchs zur Abschätzung der Rissauffangzähigkeit

Application of Charpy V‐notch testing to estimate the crack‐arrest toughness Modern structural integrity assessment relies upon fracture mechanics, thus utilizing fracture mechanical parameters describing the material fracture resistance against crack initiation and crack propagation as well as the material crack‐arrest behaviour. However, crack‐arrest fracture toughness values are usually difficult and expensive to determine. In this paper correlations are proposed for estimating the nil‐ductility temperature (T_NDT) and the crack‐arrest fracture toughness (K_Ia) from a transition temperature, based on instrumented Charpy‐V crack‐arrest load information. The transition criteria used are the 4 kN crack‐arrest force and the mean crack‐arrest fracture toughness of 100 MPa√m according to the master curve approach. Correlations between transition temperatures, T(F_a = 4 kN), T(K_Ia), and T_NDT, which were proposed for various structural steels, work very well for the 18Ch2MFA material.     

A continuum damage mechanics model for crack initiation in mixed mode ductile fracture

This paper presents the development of a fracture criterion based on the postulation that the threshold condition of crack initiation in mixed mode ductile fracture is satisfied when the overall damage w in an element at the prospective direction of crack path reaches its critical value w_c. The validity of the proposed criterion is checked by predicting the fracture loads of thin aluminium plates containing an isolated crack inclined at the angle of =30, 45, 60 and 75 degrees and the predicted loads are compared satisfactorily with those determined experimentally. The analysis is performed based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors, thus providing additional proof of the consistency, applicability and versatility of the model. When the fracture loads of the mixed mode plates calculated using conventional fracture mechanics are compared with those determined using the proposed damage model, a maximum close to 30 percent over-estimation of the loads from the conventional approach is observed as opposed to within 7 percent discrepancy between the computed and measured fracture loads using the damage approach. The observation reveals the importance of including damage consideration in any ductile fracture analysis.The effect of varying damage coefficients on the fracture loads is examined and it is found that the crack initiation load decreases with the increase of anisotropic damage coefficient.     

Assessment of the fracture toughness of cast steels

Estimates of the fracture toughness in terms of the critical stress intensity factorsK _C andK _IC are made for a 1Cr steel, a 1/2Cr-1/2Mo-1/4V steel, a 1 1/2Mn-Ni-Cr-Mo steel and a 1 1/2 Ni-Cr-Mo steel all in cast form. The methods used are linear elastic fracture mechanics,J-integral and crack opening displacement methods. The last two methods are applied in combination with an electrical potential method to detect the initiation of fracture.     

Fatigue Life Estimation of Structural Components Using Macrofibre Composite Sensors

Abstract: Recently, a number of different structural health monitoring (SHM) techniques have been developed for the online inspection of air, land and sea engineering structures. Various smart materials are employed for detecting eminent damage in situ. Fatigue cracks in structural components are the most common cause of structural failure when exposed to fatigue loading. Fatigue design of structural components is typically accomplished either using a set of stress cycle (S‐N) data obtained from prior fatigue tests or using the fracture mechanics approach. The fracture mechanics approach considers the fatigue life of structures as a summation of crack initiation life and crack propagation life. The stress intensity factor (SIF) is required for the estimation of fatigue crack propagation life from the linear elastic fracture mechanics (LEFM) perspective. However, the accurate prediction of the SIF is difficult especially when the geometry or the boundary conditions of a structure becomes complex. In this study, a SHM application of macrofibre composite (MFC) sensors is presented. A set of MFC sensors is used for the real‐time measurement of the SIF. The measured values of the SIF are later used for the prediction of the crack propagation life. The impedance‐based SHM technique using the same set of MFC sensors is employed for the detection of crack initiation life.