Local Stress Intensity Research Articles

3D predictions of the local effective stress intensity factor as the fatigue crack propagation driving force

The objective of this study is to develop a numerical tool using the commercial software, Abaqus and Python, to predict the fatigue crack front shape while taking into account the influence of plasticity induced crack closure on crack propagation in three Dimensional (3D) structures. In this aim, a 3D model of a compact tension specimen made out of stainless steel 304L, and subjected to a constant loading scheme, is proposed. The crack propagation is considered to be driven by the stress fields developed in the vicinity of the crack tip and thus by the stress intensity factor K. Two parallel simulations are used: an elastic simulation intends to calculate the local maximum stress intensity factor while the other, an elasto-plastic one, aims at obtaining the plastic wake and the resulting crack closure load. The results of both simulations are combined in order to constitute the effective stress intensity factor range, which is in turn used, along with Paris law, to calculate the crack propagation along the thickness. The local crack advancements obtained allow to construct the new crack front. Finally, a node release technique is used with geometry remeshing to issue new iterations with new boundary conditions that respond to the changes in the crack front. The procedure is repeated until the stabilization of the effective stress intensity factor values all along the specimen thickness is reached. The results obtained are compared with previously issued experimental results, showing very good results in small scale yielding and beyond that a large dependency on the plastic zone size developed in the neighborhood of the crack front.

Closed-form solutions for modified polarization saturated models in two unequal collinear cracked piezoelectric media considering coalesced interior zones

In this paper, we present polynomial varying modified polarization saturation models for semipermeable two unequal collinear cracks with coalesced interior zones in piezoelectric media. Under the influence of far-field electromechanical loadings, the cracks situated in an infinite arbitrary polarized piezoelectric media are opened in self-similar manner, forming a strip saturated zone in front of the cracks-tips. Here, we modify the polarization saturation (PS) model in a way by arresting these zones with linear, quadratic and cubic polynomials types variable saturated conditions in place of constant saturated condition. Such modified PS models are, by using complex variable and Stroh formalism techniques, firstly reduced into simultaneous non-homogeneous Riemann–Hilbert problems in complex variable field functions, and the corresponding solutions are then obtained. The closed-form solutions for standard fracture parameters such as saturated zone lengths, local stress intensity factors(LSIFs), crack opening displacements and crack opening potentials are derived. Numerical studies are illustrated for all the modified PS models by analyzing the effects on saturated zone lengths and LSIFs with respect to the variations in electrical loadings, poling direction and crack lengths. Moreover, the obtained results are compared with the results of PS model. The study concludes that the saturated zone lengths and LSIFs increase significantly with the increase in degree of polynomial varying saturation condition.

Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.

Analysis and verification of a biomimetic design model based on fish skin

Many biological architectures are Bouligand structures, which comprise uniaxial fiber layers stacked in a periodic helical arrangement and are characterized by high damage resistance. As an effective flexible protective structure, fish skin is a Bouligand structure that protects the body while ensure flexibility during swimming and predation. In this paper, an analytical model inspired by fish skin is established based on previous studies, and the parameters for describing crack growth are determined. Then, mathematical expressions for the local stress intensity factors and plastic zone are used to predict how the helical stacking angle α influences the crack propagation. The results show that crack deflection and twisting improve the fracture toughness of the composite structure greatly, with the optimal fracture toughness being that for α = 60° – 70°. Moreover, biomimetic flexible composite structures inspired by fish skin are produced using silicone and Kevlar fibers. Scanning electron microscopy is used to observe the cross-sectional morphology of the composite structures, showing that the interfaces between the silicone and Kevlar fibers are highly compact. Results from experimental impact tests agree well with the predicted results.

Complex variable solution for mode-III quadratically varying PS model in piezoelectric media

Complex variable technique and extended Stroh formalism approach are applied to develop the closed-form solutions for mode-III quadratically varying polarization saturation (PS) model in an infinite piezoelectric media. A semipermeable centre crack problem is considered for study under the influence of out of plane far-field mechanical loading and in-plane electrical displacement loading. Similar to PS model, the electrical yielding zones or saturated zones are considered just infront of the crack-tips in the form of a strip. But in place of constant PS condition imposed on yielding zones, the quadratically varying PS condition is considered for study. Mathematically, this problem reduces into simultaneous non-homogeneous Riemann-Hilbert problems which are solved by finding the solutions of involved singular integrals. Hence, some standard fracture parameters are derived in explicit forms such as saturated zone lengths, crack sliding displacement, crack potential drop and local stress intensity factor. Also, the comparative studies for quadratically varying PS model and PS model are presented graphically.

Effect of cyclic heating on subcritical crack growth of rock beams under four-point bending test

This study considers the effects of cyclic differential heating on the velocity of the subcritical crack growth (SCG) from a central notch in rock beams under four-point bending test. Beams of both Carrara marble and Fujian granite are subjected to non-uniform heating, with heating from the top surface containing the notch (at about 60° Celsius) and with cooling to the bottom side with no notch (at about 25° Celsius). Beams are heated for 7–188 days before they are subject to constant load creeping test under four-point bending configuration, and the compliance method is used to interpret crack growth from the crack mouth opening displacement (CMOD). The compliance method is verified by using acoustic emissions from cracking events together with simultaneous microscopic observations. It was discovered that a microcrack processing zone (PZ) was observed in the form of white patches ahead of the notch tip during the creeping test, followed by sudden jumps of macrocrack growth. Linear elastic fracture mechanics (LEFM) is used to calculate the local stress intensity factor, which is then further related to crack growth velocity, through the commonly adopted power law. After the application of non-uniform cyclic heating, the P-wave velocity of Fujian granite increases (due to microcrack closure) whilst that of Carrara marble decreases (due to parallel crack formation). The SCG parameters in the power law (power index n and threshold velocity v0) are obtained. There is no clear trend in the variation of the SCG parameters with the number of heating cycles. However, these parameters are used to simulate subcritical crack growth velocity for both heated and unheated specimens. In the light of fracture mechanics analysis, we conclude that Fujian granite is clearly preferable to Carrara marble in making rock panels on cladding of buildings.

Holistic Approach on the Research of Yielding, Creep and Fatigue Crack Growth Rate of Metals Based on Simplified Model of Dislocation Group Dynamics

The simplified model of numerical analyses of discrete dislocation motion and emission from a stressed source was applied to predict the yield stress, dislocation creep, and fatigue crack growth rate of metals dominated by dislocation motion. The results obtained by these numerical analyses enabled us to link various dynamical effects on the yield stress, dislocation creep, and fatigue crack growth rate with the experimental results of macroscopic phenomena, as well as to link them with theoretical results obtained by the concept of static, continuously distributed infinitesimal dislocations for the equilibrium state under low strain or stress rate conditions. This will be useful to holistic research approaches with concern for time and space scales, that is, in a time scale ranging from results under high strain rate condition to those under static or low strain rate condition, and in a space scale ranging from meso-scale to macro-scale mechanics. The originality of results obtained by these analyses were found by deriving the analytical formulations of number of dislocation emitted from a stressed source and a local dynamic stress intensity factor at the pile-up site of dislocations as a function of applied stress or stress rate and temperature material constants. This enabled us to develop the predictive law of yield stress, creep deformation rate, and fatigue crack growth rate of metals dominated by dislocation motion. Especially, yielding phenomena such as the stress rate and grain size dependence of yield stress and the delayed time of yielding were clarified as a holistic phenomenon composed of sequential processes of dislocation release from a solute atom, dislocation group moving, and stress concentration by pile-up at the grain boundary.

Fatigue analyses and life predictions of laser-welded lap-shear specimens made of low carbon and high strength low alloy steels

This paper first presented fatigue analyses of dissimilar laser welds (LWs). Laser welded (LWed) lap-shear (LS) specimens made of low carbon (LC) and high strength low alloy (HSLA) steel sheets were used in quasi-static and fatigue tests. Failure loads and fatigue data of LWed LS specimens were obtained. The LWs before and after failure were examined by optical and scanning electron microscopes. Three failure modes and corresponding failure mechanisms were obtained in quasi-static, high-cycle and low cycle conditions. The quasi-static failure mode was controlled by necking failure in base metal of LC steel. The low-cycle fatigue failure mode was controlled by upper sheet separation in heat affected zone (HAZ) of LC steel, while the high-cycle fatigue failure mode was controlled by lower sheet separation in HAZ of HSLA steel. Finite element models of LWs with original cracks and finite kinked cracks in LS specimens were developed to obtain the corresponding global and local stress intensity factors (SIFs), respectively. Finally, the fatigue lives predicted by the fatigue model based on the local SIF solutions and Paris law agreed well with the experimental results.

Fracture–Mechanical Assessment of the Effect of Defects on the Fatigue Lifetime and Limit in Cast and Additively Manufactured Aluminum–Silicon Alloys from HCF to VHCF Regime

Aluminum–silicon alloys are commonly used in die-cast and additively manufactured (AM) light-weight components due to their good processability and high strength-to-weight ratio. As both processing routes lead to the formation of defects such as gas and shrinkage porosity, a defect-sensitive design of components is necessary for safe application. This study deals with the fatigue and crack propagation behavior of die-cast alloy AlSi7Mg0.3 and additively manufactured alloy AlSi12 and its relation to process-induced defects. The different porosities result in significant changes in the fatigue stress-lifetime (S–N) curves. Therefore, the local stress intensity factors of crack-initiating defects were determined in the high and very high cycle fatigue regime according to the fracture mechanics approach of Murakami. Through correlation with fatigue lifetime, the relationship of stress intensity factor (SIF) and fatigue lifetime (N) could be described by one power law (SIF–N curve) for all porosities. The relationship between fatigue limit and defect size was further investigated by Kitagawa–Takahashi (KT) diagrams. By using El Haddad’s intrinsic crack length, reliable differentiation between fracture and run out of the cast and AM aluminum alloys could be realized. SIF–N curves and KT diagrams enable a reliable fatigue design of cast and AM aluminum alloys for a finite and infinite lifetime.

Numerical assessment of the effects of microcrack interaction in AM components

A combined analytical–numerical method to study the effects of linear microcracks and their interaction in additively manufactured components is presented. The 2-D method combines an analytical technique to solve the interaction of microcracks and a numerical RVE type technique to represent the microcracking within a finite element framework using Abaqus finite element software. The method is applied to both a unit cell and test specimen type geometries containing defect patterns generated based on general trends reported for AM materials. The approach is able to determine the local stress intensity factors for each microcrack and their stiffness degradation effects in the continuum. Parallel defect patterns, such as co-oriented lack-of-fusion defects between build layers in AM materials, induce the greatest interaction effects while overall interaction effects in random patterns tend to cancel out. Stacked surface defects produce shielding effects on each other, which may cause a neighbouring subsurface defect to be more critical than the surface defects. The results show that the common geometrical interacting defect re-characterisation rules may provide an incorrect prediction of the failure origin. Finally, the applicability of the method is demonstrated with an example AM component.

Relationship Between Functional Fatigue and Structural Fatigue of Iron-Based Shape Memory Alloy FeMnNiAl

Utilizing FeMnNiAl single crystals subjected to fatigue loading, we make the important observation that the crack nucleation from the notch and the ensuing crack trajectory follows the most favorable martensite variants. These variants form in an asymmetric pattern with respect to the crack plane because of the underlying elastic anisotropy which is accounted for in the driving force analysis of the fatigue cracks. When the recoverable strain on a particular variant is exhausted, new variants are activated; this in turn changes the crack path. The activation of new variants also results in transient deceleration of the fatigue crack growth rates and upon subsequent growth, fatigue crack growth trends merge with the steady state behavior. Two surface analysis using FIB/TEM facilitated the unambiguous identification of the specific martensite variants responsible for fatigue crack growth. Displacement fields obtained via digital image correlation allowed for the determination of the local stress intensity which is inevitably affected by the activation/arrest of martensite variants. Hence, we make a direct link between the complex functional fatigue behavior and the fatigue crack growth behavior. Overall, the results show the steps to be considered to develop a framework for understanding fatigue crack growth response of shape memory alloys.

3D effects on Fracture Mechanics

Simplified mathematical models are extremely useful for understanding and characterizing physical phenomena; this is the case of plane (stress/strain) elasticity, which has been the main analytical framework of Fracture Mechanics since its origins. Bowed crack fronts in thin sheets and plates, unpredicted fatigue crack paths, and crack initiation as well as brittle fracture location are only examples of fracture mechanisms not completely explained by the classical closed form 2D solutions, e.g. Westergaard’s solution. This paper aims to provide a brief review on 3D effects on the brittle fracture behavior of linear, elastic, homogeneous and isotropic solids in presence of cracks or notches, under the hypothesis of small scale plasticity (LEFM). We overview the main theoretical and numerical results on coupled modes of fracture, i.e. coupling of shear (Mode II) and out-of-plane (Mode III) modes, due to three-dimensional effects and on 3D vertex singularities close to a corner point generated by the intersection of a crack/notch front with free surfaces. We also address recent theoretical-numerical studies and inconsistencies on the relation of crack (notch) tip stress singularities, usually characterized by local (notch) stress intensity factors, in the vicinity of a corner point and far away from it. Despite numerous works have attempted to interpret finite element and analytical results, no consensus exists on the behaviour of the 3D stress field near a vertex of cracked/notched solids; a unifying theory, able to guarantee the extension of the results of experimental tests prescribed by standards, based on the 2D theory of elasticity, to real cases, is still required.

Experimental investigation on local shear stress and turbulence intensities over a rough non-uniform bed with and without sediment using 2D particle image velocimetry

The current work focuses on locally resolving velocities, turbulence, and shear stresses over a rough bed with locally non-uniform character. A nonporous subsurface layer and fixed interfacial sublayer of gravel and sand were water-worked to a nature-like bed form and additionally sealed in a hydraulic flume. Two-dimensional Particle Image Velocimetry (2D-PIV) was applied in the vertical plane of the experimental flume axis. Runs with clear water and weak sediment transport were done under slightly supercritical flow to ensure sediment transport conditions without formation of considerable sediment deposits or dunes. The study design included analyzing the double-averaged flow parameters of the entire measurement domain and investigating the flow development at 14 consecutive vertical subsections. Local geometrical variabilities as well the presence of sediment were mainly reflected in the vertical velocity component. Whereas the vertical velocity decreased over the entire depth in presence of sediment transport, the streamwise velocity profile was reduced only within the interfacial sublayer. In the region with decelerating flow conditions, however, the streamwise velocity profile systematically increased along the entire depth extent. The increase in the main velocity (reduction of flow resistance) correlated with a decrease of the turbulent shear and main normal stresses. Therefore, effects of rough bed smoothening and drag force reduction were experimentally documented within the interfacial sublayer due to mobile sediment. Moreover, the current study leads to the conclusion that in non-uniform flows the maximum Reynolds stress values are a better predictor for the bed shear stress than the linearly extrapolated Reynolds stress profile. This is an important finding because, in natural flows, uniform conditions are rare.

A completely coated wedge crack interacting with a screw dislocation

We employ conformal mapping and analytic continuation to study the elastic field induced by a screw dislocation interacting with a completely coated semi-infinite wedge crack under mode III loading conditions. The screw dislocation can be located either inside the matrix or in the coating itself. Explicit expressions for the local wedge stress intensity factor and the image force acting on the screw dislocation are obtained. The dislocation emission criterion from the completely coated wedge crack is established.

On the behaviour of non-propagating cracks in steel and aluminium castings

Casting defects as well as sharp notches can serve as initial points for fatigue cracks under cyclic loading. On the contrary, the cyclic material crack resistance counteracts to crack propagation. Hence, an incipient crack can arrest completely, even though a constant cyclic load is applied. Considering a short propagating crack, the local stress intensity factor, which represents the crack growth driving force, increases due to the crack extension, yet crack arrest may occur. Such an arresting of growing cracks can be traced back to an increase of the materials resistance in terms of crack closure effects. This paper deals with the evaluation of the cyclic short crack behaviour and the assessment of non-propagating cracks for cast aluminium and cast steel in terms of the Frost diagram. At first, single edge notched bending specimens are machined out of both cast materials and investigated in regard to their fracture mechanical short and long crack growth behaviour under varying stress ratios. Moreover, the data is analysed in terms of the short crack resistance (R-curve) and the subsequent long crack growth behaviour. Secondly, detectable surface porosity defects, regarding the aluminium material, and sharp surface notches, as in case of cast steel, are investigated by a linear elastic finite-element simulation to evaluate the local stress concentration factors numerically. Finally, Frost diagrams are set up for both materials and well approved by the detected non-propagating cracks. A final comparison of the investigated fatigue test data points and the Frost diagrams reveals a sound agreement validating the applicability of the presented approach.

The Study of Local Stress Intensity Factors for Kinked (and Branched) Cracks in Commonly Used Spot Weld Specimens

The Study of Local Stress Intensity Factors for Kinked (and Branched) Cracks in Commonly Used Spot Weld Specimens

Analytical solution for two equal collinear modified strip saturated cracks in 2‐D semipermeable piezoelectric media

AbstractAn analytical solution and study is presented for two equal collinear cracks in 2‐D semipermeable piezoelectric media based on modified strip saturation models. The constant saturated condition defined in strip saturation model is modified here by considering the symmetric and polynomial varying saturation conditions. These proposed saturated conditions are multiplicative of saturated electric displacement value and polynomial (constant to cubic order) of a variable defined as ratio of distance of a point on saturated zone length to the extended half‐crack length. Moreover, these are interpolated on the basis of possible saturated values near the crack‐tips and zone tips. To present the analytical study, a problem of two cracks of equal length situated in series is considered in 2‐D arbitrary polarized infinite piezoelectric domain subjected to semipermeable crack‐face and electromechanical loading conditions. Applying the extended Stroh formalism and complex variable approach, these problems are mathematically modeled into non‐homogeneous Riemann Hilbert problems in terms of unknown complex functions representing stress and electric displacement components at any point within the domain. Using Muskhelishvili [1] and Collin's [2] mathematical techniques, these complex functions are obtained from the developed non‐homogeneous Riemann Hilbert problems. Hence, the explicit expressions for saturated zone lengths (inner and outer), crack opening potentials (COPs), crack opening displacements (CODs) and local stress intensity factors (LSIFs) are obtained. Further, the impact of polynomial varying saturated conditions is highlighted on these fracture parameters with respect to inter crack space distance, crack‐face conditions, polarization angle by presenting the numerical applications in infinite 2‐D PZT‐4 media.

A nondestructive raman spectra stress 2D analysis for the pressure sensor sensitive silicon membrane

The residual stresses introduced by the bonding process has become a key effect for the MEMS product yield improvements. Many in-situ stress measurements have to destruct the devices. Raman spectroscopy is a nondestructive inelastic scattering measuring. Interpreting the silicon Raman frequency shifting can describe the stress location and intensity quantitatively in the lattice. The confocal microscopic observation can realize micrometer scale resolution. However, the limited visual field cannot provide the device stress distribution overview. In the meantime, the microscope loading platform displacement (only 100 μm) will introduce severe random errors (4 ± 1 μm) in the overlapping movements. Since the local stress intensity could be converted into a RGB gray pixel. Through the image mosaic algorithms, the measured local residual stress distribution maps (750 μm × 160 μm) could be stitched to an enlarged stress distribution map (750 μm × 340 μm). This methodology could not only expand the stress inspection overview(60 ± 2%), but also examine and eliminate the displacement random errors. The analysis results showed that the residual stresses were about 70 ± 5% of the simulation value. The uniform difference between the measured and simulated values indicated a trustable stress analysis.

Revealing the inhibition mechanism of grain size gradient on crack growth in gradient nano-grained materials

Gradient nano-grained (GNG) materials, in which grain size changes from nano-scale in the surface to micro-scale in the core, have shown superior fatigue property, good strength and ductility. However, crack growth behaviors of GNG materials are studied hardly. In this work, the effect of grain size gradient on crack growth is investigated to reveal the inhibition mechanism of crack growth in GNG materials. The developed model employs a distributed dislocation method to model the evolution of plastic zone. The influence of grain size gradient on the distribution of dislocations in grains and the local stress intensity factor is analyzed. The results show that the sizes of dislocation zone and dislocation-free zone in grains become larger as the gradient of grain size increases. The number of dislocations emitted from the crack tip increases with the grain size gradient increasing, so the shielding effect of emitted dislocations on the crack growth increases and crack blunting becomes more serious. This means that a sharper grain size gradient inhibits the crack growth more effectively. The results in this paper are important for understanding the fracture behaviors of materials with grain size gradient and are helpful for material design and structural optimization.

Three-dimensional characterization of desiccation cracking behavior of compacted clayey soil using X-ray computed tomography

The shrinkage potential of clayey soils dominates their volumetric deformation and microscopic cracking behavior during desiccation processes and has profound practical consequences. To investigate the evolution of desiccation crack network in the compacted clayey soil, we apply a noninvasive approach integrating X-ray computed tomography (CT) and digital image processing technique. Representative geometrical parameters including soil mass area, shrinkage strain, crack ratio, average crack width, total crack length, and crack segment number are acquired from image analysis results to quantify the morphological evolution of desiccation crack patterns. Experimental observations show that cracks initiate at surface, propagate both laterally and downward into the soil body, and transit into massive networks due to coalescence and bifurcation. Quantitative analyses reveal the strong dependence of geometrical parameters on water loss through evaporation. The shrinkage and cracking potential of the clayey soil specimen attenuate with the decreasing water content, which significantly reduces the growing trend of geometrical parameters during the posterior stage of desiccation. The spatial variation of crack network evolutions under drying results from intrinsic soil microstructural heterogeneity and suction capillary-induced local stress intensity. The proposed integrated approach is of great significance to characterize three-dimensional soil desiccation crack patterns and brings new perspectives into the study of the hydro-mechanical behavior of clayey soils.