A non-local stress failure condition for structural elements under multiaxial loading

A non-local stress condition for crack initiation and propagation is proposed and applied to several particular cases, such as plate with wedge-shaped notch, elliptical hole and hyperbolic notch. Brittle failure initiation for notched elements under complex loading (Modes I and II) is studied in detail. A value of critical load and crack orientation is predicted from the non-local condition, which is applicable to both regular and singular stress concentrations.     

A phenomenological analysis of Mode I fracture of adhesively-bonded pultruded GFRP joints

The fracture behavior of adhesively-bonded pultruded joints was experimentally investigated under Mode I loading using double cantilever beam specimens. The pultruded adherends comprised two mat layers on each side with a roving layer in the middle. An epoxy adhesive was used to form the double cantilever beam specimen. The pre-crack was introduced in three different depths in the adherend in order to induce crack initiation and propagation between different layers and thus investigate the effect of these different crack paths on the strain energy release rate. Short-fiber and roving bridging increased the fracture resistance during crack propagation. Specific levels of critical strain energy release rates could be attributed to each of the crack paths, with their levels depending on the amount of short-fiber bridging and the presence of a roving bridge. The different levels of critical strain energy release rate could be correlated to the morphology of the fracture surface and the strain energy release rate can thus be determined visually without any measurement.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

On The Use Of Vector J-Integral In Crack Growth Criteria For Brittle Solids

In this paper the criterion for crack-growth in solids is investigated on the basis of the concept of potential energy release rate. The expressions for path-independent vector integral J_i (i = 1,2) are derived for brittle crack growth. The relationship is then established between the value of the path-independent vector integral J_i and the potential energy release rate for crack growth in an arbitrary orientation. This allows the prediction of crack re-orientation angles on the basis of the maximum energy release rate (MERR) criterion. The crack growth angle is determined analytically as a function of (). This result is compared with other theoretical formulations of crack growth criteria, as well as with experimental results reported in the literature, and good agreement is found. The formulation provides a rigorous basis for numerical modelling of the processes of crack initiation and propagation.     

Using the X-FEM method to model the dynamic propagation and arrest of cleavage cracks in ferritic steel

Although initiation criteria have been the subject of many publications, the phenomena associated with the propagation and arrest of brittle cracks have not. To be able to predict the dynamic behaviour of cleavage cracks, we made a series of experiments and associated numerical studies. Tests of crack propagation and arrest were carried out on specimens of two different geometries (Compact Tension and compression ring) made of the 16MND5 ferritic steel of which French nuclear reactor vessels are constructed. The elastic-viscoplastic behaviour of this material was characterised and its nature was taken into account in the numerical simulations. The eXtended Finite Element Method (X-FEM) was developed in CAST3M finite element analysis software to enable fine, effective modelling of crack propagation. Propagation models based on principal stress were studied and it was found that critical cleavage stress depended on loading rate. The use of criteria calibrated for Compact Tension specimens gave excellent results in predictive calculations for similar specimens, and also for compression rings in both mode I and mixed-mode. The speed and path of crack predicted with the numerical simulations were in close agreement with the experimental results.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination experiments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack propagation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then estimated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and the crack propagation along the interface, is governed by elasto-plastic normal stress on the order of 10 nm.     

Branch cracking and debonding at an end of a rigid stiffener under anti-plane shear stress

A semi-infinite body with a rigid stiffener on a part of the surface under uniform anti-plane shear stress is considered. This is a mixed boundary value problem, and a closed and exact solution is obtained. Stress concentration occurs at the ends of the stiffener; therefore a crack or a debonding may occur at the end of the stiffener. This paper investigates the competition between a crack or a debonding occurrence. It also investigates how far the debonding will extend. The maximum strain energy release rate is used as criterion for detecting a crack and a debonding initiation. Also the strain energy release rate just after crack initiation is investigated and the crack initiation angle is 140.8°. As the applied load, the following three kind of loading conditions are considered; constant loading, increasing loading and small cyclic loading.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Effect of the stress distribution in simple welded specimens and complex components on the crack propagation life

While a long stable crack propagation phase was observed during experiments of complex welded components, very conservative estimations of the fatigue life were achieved in the past. The difference was explained by the stress gradient occurring over the plate thickness. This paper deals with numerical crack propagation simulations which were performed for geometrically different variants. The variants differ in global geometry, boundary conditions and weld shape. The analyses aim to investigate how the crack propagation is altered if the structural configuration gets more complex. In conclusion, the stress gradient over the plate thickness, the effective plate thickness due to vertical web plates and high notch effects slow down the crack propagation rate if the same stress value being effective for fatigue appears at the weld toe. Thereby, the load-carrying grade of the weld, the weld flank angle and the geometrical configuration also have an impact on both the notch effect and the local stress concentration.     

MIXED MODE FATIGUE CRACK THRESHOLDS FROM BENDING AND CYCLIC TORSION OF A PLATE

The effects of plate thickness and crack shape on the threshold condition for crack propagation under cyclic bending or torsion, was studied using a through or a surface pre-crack in a carbon steel plate of various thicknesses. It was concluded that the magnitude of the frictional stress acting on the crack surface at the propagation threshold under cyclic torsion was significantly affected by the plate thickness. An estimation method for the threshold condition for crack propagation under mixed-mode loading for a particular plate thickness was proposed on the basis of the strain energy density criterion.     

Experimental and numerical study on crack initiation under fretting fatigue loading

Press-fitted railway axles and wheels are subjected to fretting fatigue loading with a potential hazard of crack initiation in press fits. Typically, the resistance against crack initiation and propagation in press fits is investigated in full-scale tests, which procedure is both costly and time consuming. In this context, combined experimental and numerical approaches are of increasing practical importance, as these may reduce the experimental effort and, moreover, provide a basis for the transferability of experimental results to different axle geometries and materials. This study aims at evaluating stress–strain conditions under which fretting fatigue crack initiation is likely to occur. Experiments on small-scale specimens under varying fretting fatigue load parameters and their finite-element modelling to characterize the resulting stress–strain fields are performed. Subsequently, different multiaxial fatigue parameters are applied to predict crack initiation under fretting fatigue conditions.     

High-temperature ultra-high cycle fatigue damage of notched single crystal superalloys at high mean stresses

Blade nickel superalloy CMSX-4 widely used in the aero industry and its potential low cost alternative, superalloy CM186LC intended for use in the industrial gas turbines, were subjected to ultra-high-cycle fatigue at high mean stresses to model the effect of vibrations superimposed on sustained load. Circumferentially notched cylindrical specimens of single crystals with the axis orientation of [001] were tested at 850 °C in air. For small amplitudes of the cyclic stress superimposed on the sustained stress the time to fracture is slightly increasing with increasing stress amplitude. This trend is reversed for higher stress amplitudes where the time to fracture quickly decreases with increasing stress amplitude. Fatigue crack initiation and following crack propagation are here the decisive failure mechanisms. Cyclic stress component leads to the formation of persistent slip bands running through the γ matrix and the γ′ precipitates. These bands represent sites for the initiation (in interaction with casting pores and other defects) and early propagation of fatigue cracks. The early crack propagation along the slip planes is later replaced by non-crystallographic propagation of the dominant crack.     

Cyclic loadings and crystallization of natural rubber: An explanation of fatigue crack propagation reinforcement under a positive loading ratio

Natural rubber is known to have excellent fatigue properties. Fatigue crack propagation studies show that, under uniaxial tension loading, fatigue crack growth resistance increases with the loading ratio, even if the peak stress increases. Studies dealing with crack initiation confirm this trend. If strain induced crystallization is believed to play a major role in this reinforcement process, it is not clear yet by which mechanism this reinforcement takes place. Using SEM investigation, it is shown here that the reinforcement process is associated with strong crack branching in the crack tip region. From experimental results it is shown that under particular reinforcing loading condition a cyclic strain hardening process can be observed on the natural rubber which is able to overcome classically observed softening effects. A cumulative strain induced crystallization process is proposed to explain the stress ratio effect on fatigue crack initiation and propagation properties of natural rubber.     

Stress gradient effect on the crack nucleation process of a Ti–6Al–4V titanium alloy under fretting loading: Comparison between non-local fatigue approaches

This study focuses on the stress gradient effect regarding the crack nucleation of a cylinder/plane Ti–6Al–4V titanium alloy contact under low cycle fatigue (LCF) fretting loading. Several local and non-local analytical approaches were compared to predict experimental results. The first part of the study presents fretting nucleation boundaries for three different cylinder radii in the partial slip regime. In the next part, the Crossland and Papadopoulos multi-axial fatigue criteria are computed and compared. Finally, local and non-local fatigue approaches are compared. Square constant volume, critical distance and weighted function approaches have been compared.The methodology used covers a large range of stress gradients. The impact of varying the stress gradients is that the larger the stress gradient, the larger the difference between experiments and local stress fatigue predictions. A Crossland local form was applied to confirm that a local stress fatigue analysis cannot predict the fretting cracking risk. Three non-local approaches were carried out, and the results allowed the proper prediction of the empirical thresholds with a 3–5% margin of error. The positive results obtained helped to select a multi-axial fatigue criterion and a non-local approach which take into account the gradient effect of contact fretting behavior.     

Effect of loading rate on crack velocities in HSC

This paper presents the recent results of an experimental program aimed at disclosing the loading rate (loading-point-displacement rate) effect on the crack velocity in high-strength concrete (HSC). Eighteen three-point-bend tests were conducted using either a servo-hydraulic machine or a self-designed drop-weight impact device. Four strain gauges mounted along the ligament of the specimen were used to measure the crack velocity. Six different loading rates were applied, from 10⁻⁴ mm/s to 10³ mm/s (average strain rate from 10⁻⁶ to 10⁻¹ s⁻¹), i.e., a low loading-rate range (5.50 × 10⁻⁴ mm/s, 0.55 mm/s and 17.4 mm/s) and a high loading-rate range (8.81 × 10² mm/s, 1.76 × 10³ mm/s and 2.64 × 10³ mm/s). At low loading rates, the crack propagates with increasing velocity. Under high loading rates, the crack propagates with slightly decreasing velocity, though the maximum crack speed reached up to 20.6% of the Rayleigh wave speed of the tested HSC. In addition, the loading-rate effect on crack velocities is pronounced within the low loading-rate regime, whereas it is minor under the high loading-rate range.     

Simulation of brittle and ductile fracture in an impact loaded prenotched plate

We analyze the initiation and propagation of a crack from a point on the surface of a circular notch-tip in an impact loaded prenotched plate. The material of the plate is assumed to exhibit strain hardening, strain-rate hardening, and softening due to the rise in temperature and porosity. The degradation of material parameters due to the evolution of damage in the form of porosity is considered. Brittle failure is assumed to initiate when the maximum tensile principal stress at a point reaches a critical level. Ductile failure is assumed to ensue when the effective plastic strain reaches a critical value. A crack initiating from the node where a failure first occurs is taken to propagate to the adjacent node that has the highest value of the failure parameter (the maximum tensile principal stress or the effective plastic strain). The opening and propagation of a crack are modeled by the node release technique. Surface tractions and the normal component of the heat flux are taken to be null on the newly created crack surfaces. For the brittle failure, the stress field around the crack tip resembles that in mode-I deformations of a prenotched plate loaded in tension. The distribution of the effective plastic strain in a small region around the surface of the notch-tip is not affected much by the initiation of a ductile fracture there except for a shift in the location of the point where the effective plastic strain is maximum. The initiation of the ductile failure is delayed when a crack is opened at the point where the brittle failure ensues.     

Automated dynamic fracture procedure for modelling mixed-mode crack propagation using explicit time integration brick finite elements

Several fracture codes have been developed in recent years to perform analyses of dynamic crack propagation in arbitrary directions. However, general-purpose, commercial finite-element software which have capabilities to do fracture analyses are still limited in their use to stationary cracks and crack propagation along trajectories known a priori . In this paper, we present an automated fracture procedure implemented in the large-scale, nonlinear, explicit, finite-element code DYNA3D which can be used to simulate dynamic crack propagation in arbitrary directions. The model can be used to perform both generation- and application-phase simulations of self-similar as well as non-self-similar dynamic crack propagation in linear elastic structures without user intervention. It is developed based on dynamic fracture mechanics concepts and implemented for three-dimensional solid elements. Energy approach is used in the model to check for crack initiation/propagation. Dynamic energy release rate and stress intensity factors are determined from far-field finite-element field solutions using finite-domain integrals. Fracture toughness is input as a function of crack-tip velocity, and when the criterion for crack growth is satisfied, an element deletion-and-replacement re-meshing procedure is used along with a gradual nodal release technique to update the crack geometry and model the crack propagation. Direction of crack propagation is determined using the maximum circumferential stress criterion. Numerical simulations of experiments involving non-self-similar crack propagation are performed, and results are presented as verification examples.     

Numerical analysis of dynamic T stress of moving interfacial crack

A method to extract dynamic T stress term of moving interfacial crack is proposed. Anisotropic bimaterial which has subsonic crack propagation is considered, and interaction energy method is applied. Stress fields by the constant T stress and stress fields by the point force moving with the crack are obtained by using the series expansion method and Stroh formalism. J based interaction energy (J^I) between the constant T stress and the point force is calculated by Yeh formulation and the relation between interaction energy and T stress is obtained. Energy release rate and T stress of a moving interfacial crack are calculated numerically. Elastodynamic finite element code is developed to investigate fracture parameters for the propagating crack. Four nodes linear elastodynamic element is used and Newmark formulae are applied to integrate displacement and velocity. Node release method is adapted to simulate crack propagation along the interface. The energy release rate is calculated in the area moving with crack. T stress term is calculated from the interaction energy with a stress field formed by the moving point force. Five examples are solved to show the validity and time history of energy release rate and T stress. The energy release rate calculated from numerical analysis agrees well with an analytic solution and experimental results. The T stress of homogeneous specimen under the steady state condition shows a slightly different value compared with the stationary result. It is observed that the T stress of polymethyl methacrylate–steel specimen shows continuous change and the T stress of aluminum-polymethyl methacrylate specimen shows discontinuous jump when the initial crack initiates. From the result of the variation of T stress, the effect of T stress on the stability of crack propagation is observed.