Stress multiaxiality factor for crack growth prediction using the strain energy density theory

The multiaxiality factor defined as the ratio of the von-Misses equivalent stress to the volumetric stress has been reported to be related to the initiation and progression of failure in structures. It is demonstrated in the present paper that the location around the crack tip where the multiaxiality factor obtains minimum value is an indicator of the direction of minimum material fracture resistance for crack propagation. It is also proposed that the location along the direction of crack propagation path where multiaxiality factor obtains minimum value is considered as the critical distance away from the crack tip, where the strain energy density should be evaluated and compared to its critical value. Theoretical predictions correlate well with the test results for the investigated cases.     

Effect of weld size on fatigue crack growth behaviour of cruciform joints by strain energy density factor approach

The effect of weld size on fatigue crack growth behaviour of cruciform joints containing lack of penetration defect has been analysed by using the strain energy density factor concept. Load carrying cruciform joints were fabricated from ASTM 517‘F' grade steel. Fatigue crack growth experiments were carried out in a mechanical resonance vertical pulsator (SCHENCK 200 kN capacity) with a frequency of 30 Hz under constant amplitude loading (R=0). It was found that the crack growth rates were relatively lower in the larger welds fabricated by multipass welding technique than the smaller welds fabricated by the single pass welding technique.     

Mixed mode fatigue crack growth with a sudden change in loading direction

With a sudden change in the maximum load level, there will be a corresponding change in the crack driving force regardless of whether the load is applied monotonically or cyclically. The effective strain energy density factor range ΔS_p,eff has been used to correlate mixed mode fatigue crack propagation where the crack growth direction is not known as an a priori. Examined in this work is a sudden change of load direction on fatigue crack growth while the load level remains unchanged. Yielding is assumed to be localized near the crack tip such that the crack growth behavior can be described adequately by the elastic stress field. Under the conditions investigated, minimal change on crack growth rates is observed. No firm conclusion could be drawn on deviation of crack path for the case considered.     

Mixed mode fatigue crack growth in test coupons made from 2024-T3 aluminum

In this paper, two different fracture criteria are applied to determine the crack trajectory or angle of crack propagation in test specimens containing inclined cracks emanating from open holes. Also, different crack growth rate models are assumed for each criterion. The maximum principal stress criterion is used with a crack growth-rate equation based on an effective stress intensity factor. The strain energy density criterion is used with a crack growth-rate equation corresponding to an effective strain energy density factor. The crack growth-rate models for each criterion were constructed using unpublished fatigue crack growth data for 2024-T3 aluminum.     

Subcritical and fatigue crack growth in anti-plane strain state

Assuming elastic-plastic material behavior the slow growth of Mode III crack under both monotonic and pulsating loadings is considered. Rice's idea of universal R-curve is employed while the mathematical analysis is based on the one-dimensional plasticity model suggested by Kostrov and Nikitin. Motion of a quasi-static Mode III crack is studied and the stable/unstable transition points are found through application of the final stretch failure condition proposed in 1972 by Wnuk. A logarithmic formula for fatigue crack extension rate is derived. Results are compared to other well-known solutions.     

Direction of crack growth initiation in roller contact: strain energy density criterion

Small defects or cracks near the surface of roller contact could spread and lead to failure at large. Their growth behavior depends on the rolling load, size and orientation of the initial defects, and material property in addition to friction at the contacting surfaces. Stress intensity factors K₁and K₂ are obtained for three different crack types near the surface between the roller and contacting solid. Various possible directions of crack growth initiation are obtained as the different roller loads are moved relative to the crack. The results are indicative of railway failure observed in service and are helpful to future studies on subcritical and/or critical crack growth.     

Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures

Fatigue crack growth rate depends not only on the load amplitude, but also on the morphology of crack path. The strain energy density theory has the ability to analyze crack growth rate. A strain energy density crack growth model is proposed. It can predict the lifetime of fatigue crack growth for mixed mode cracks while an equation for mode I crack is also obtained. The validity of the model is established with two cases: a center-crack panel and cracks emanating from the edge of a hole. The stress intensity factor expression for the former case is analytical while that of the latter is calculated numerically using finite elements. The results are compared with the testing data. Good agreement shows that the proposed model is useful.     

Mixed mode crack growth in curved beams with radial edge crack

Mixed mode crack growth in curved beams with radial edge crack is predicted by the prominent S-theory. An improved simple engineering method for obtaining approximate stress intensity factors of curved cracked beams is also used. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. The results are in reasonable agreement with the more accurate calculations in literature.     

Mode-I crack projection procedure using the strain energy density criterion

A practice used in linear elastic fracture mechanics is the projection of a crack onto a plane normal to the principal tensile stress axes for computing the stress intensity factor K_I. The minimum strain-energy criterion is applied for different crack configurations with the introduction of a safety factor S_i which is the ratio of the strain energy density factor of the projected crack and that of the original crack. Numerous crack configurations are investigated to illustrate the degree of conservativeness of the crack projection procedure.     

Stability analysis of crack path using the strain energy density theory

Prediction of crack growth path is a pre-requisite for estimating the final shape of broken solids and structures. Crack path in broken specimens provides information for the loading conditions just before fracture. Experiments on brittle materials, pre-cracked specimens of the same geometry under similar loading conditions, however, may yield different crack trajectories at times. The existing theories for the prediction of the crack path are based on the perturbation method combining the analytical and finite elements methods. They require a knowledge of the toughness equations. Moreover, they can only be applied to specimens with simple geometry and loadings.A different approach is used in the present work. The finite element technique is used to calculate the strain energy density (SED) contours. The predicted trajectory of the crack during unstable propagation is assumed to coincide with the minimum of the strain energy density function according to the SED criterion.The degree of crack path stability depends on the sharpness of the SED oscillations. This simple method offers a reliable prediction of the crack path stability for two as well as three-dimensional problems with complex geometry structures and arbitrary loadings. To be specific, both the TPB and DCB specimens are analysed. The findings are in good agreement with the theoretical and experimental results in the literature.     

Damage accumulation and crack growth in bilinear materials with softening: Application of strain energy density theory

A pseudo-elastic damage-accumulation model is developed by application of the strain energy density theory. The three-point bending specimen is analyzed to illustrate the crack growth characteristics according to a linear elastic softening constitutive law that is typical of concrete materials. Damage accumulation is accounted for by the decrease of elastic modulus and fracture toughness. Both of these effects are assessed by means of the strain energy density functions in the elements around a slowly moving crack. The rate of change of the strain energy density factor S with crack growth as expressed by the relation dS/da = constant is shown to describe the failure behavior of concrete. Results are obtained for different loading steps that yield different slopes of lines in an S versus a (crack length) plot. The lines rotate about the common intersect in an anti-clockwise direction as the load steps are increased. The intersect shifts upward according to increase in the specimen size. In this way, the combined interaction of material properties, load steps and specimen geometry and size are easily analyzed in terms of the failure mode or behavior that can change from the very brittle to the ductile involving stable crack growth. An upper limit on specimen or structural size is established beyond which stable crack growth ceases to occur and failure corresponds to unstable crack propagation or catastrophic fracture. The parameters that control the failure mode are the threshold values of the strain energy density function (dW/dV)_c and the strain energy density factor S_c.     

Crack growth instability studied by the strain energy density theory

The strain energy density theory has successfully been used to address the problem of material damage and structural failure in problems of engineering interest. The theory makes use of the strain energy density function, dW/dV, and focuses attention in its stationary values. The directions of crack growth and yielding are determined from the minimum and maximum values of dW/dV, respectively, along the circumference of a circle centered at the point of failure initiation. Failure by crack growth or yielding takes place when these values of dW/dV become equal to their critical values which are material constants. In the present work the basic principles of the strain energy density theory were reviewed. Furthermore, this theory was used to study three problems of structural failure, namely the problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension, the problem of fracture instability of a plate with a central crack and two notches, and the problem of unstable crack growth in a circular disc subjected to two equal and opposite forces. The results of stress analysis were combined with the strain energy density theory to obtain the whole history of crack growth from initiation to instability. A length parameter was introduced to define the fracture instability of a mechanical system. Fracture trajectories were obtained for fast unstable crack propagation.     

Mixed mode crack initiation and direction in beams with edge crack

The S-theory is applied to determine crack initiation and direction for beams with edge crack. A simple method for obtaining approximate stress intensity factors of straight cracked beams is also proposed. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. The results are in reasonable agreement with the more accurate calculations.     

Rate dependent critical strain energy density factor of Huanglong limestone

Critical strain energy density of rock can be defined as a fundamental parameter in rock fracture mechanics, an intrinsic material property related to resistance to crack initiation and propagation. By means of the three-point bending experiments, the critical strain energy density factor of Huanglong limestone was measured over a wide range of loading rates from 8.97 × 10⁻⁴ MPam^1/2 s⁻¹ to 1.545 MPam^1/2 s⁻¹. According to the approximate relationship between static and dynamic critical strain energy density factor of Huanglong limestone, relationship between the growth velocity of crack and magnitude of load is obtained. The main conclusions are summarized as follows: (1) when the loading rate is higher than 0.0279 MPam^1/2 s⁻¹, the critical strain energy density factor of rock increased markedly with increasing loading rate. However, when loading rate is lower than 0.0279 MPam^1/2 s⁻¹, the critical strain energy density factor slightly increased with an increase in loading rate. It is found from experimental results that the critical strain energy density factor is linear proportional to the exponential expression of loading rate, (2) for Huanglong limestone, when the growth velocity of crack is lower than 100 m/s, value of the maximum load was nearly a constant. However, when the growth velocity of crack is higher than 1000 m/s, value of the maximum load dramatically increases with increasing the crack growth velocity, and (3) the critical SED of Huanglong limestone is higher as the loading rate is higher.     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

Local crack tip strain behavior during fatigue crack initiation and propagation in polycarbonate

To investigate whether the two fatigue processes of crack initiation and propagation can be combined, the change of local notch root strain and its history, as well as the change of local crack tip strain and the local strain history, of a fatigued element ahead of the propagating crack tip up to failure in a polycarbonate subjected to low-cycle fatigue tests are measured by the fine grid method. As a result, the existence of a unified local strain field in which the two fatigue processes can be substantially combined is experimentally confirmed. Therefore, the local crack tip strain may be examined by a simpler, one-parameter approach for fatigue life estimation.     

Mixed mode crack initiation in piezoelectric ceramic strip

When piezoelectric ceramics are subjected to mechanical and electrical load, they can fracture prematurely due to their brittle behavior. Hence, it is important to know the electro–elastic interaction and fracture behavior of piezoelectric materials. The problem of a through crack in a piezoelectric strip of finite thickness is studied in this paper. Fourier transforms are used to reduce the problem to the solution of singular integral equations. The model technique can solve for polarization in an arbitrary direction and material anisotropy. Numerical values of the crack-tip field amplification for a piezoelectric strip under in-plane electromechanical loading are obtained. Energy density factor criterion is applied to obtain the maximum of the minimum energy density and direction of crack initiation. The influence of crack length and crack position on stress intensity and energy density factors is discussed.     

Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values minimum energy required for initiation of crack growth increases rapidly. Results received indicate a possibility to optimize energy consumption of different industrial processes connected with fracture. Much could be gained in for example drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e., frequency and amplitude of impacts, for industrial devices, e.g., bores, grinding machines, etc. and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).