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András Szekrényes - One of the best experts on this subject based on the ideXlab platform.
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Stress and fracture analysis in delaminated orthotropic composite plates using third-order shear deformation theory
Applied Mathematical Modelling, 2020Co-Authors: András SzekrényesAbstract:The third-order shear deformable plate theory is applied in this work to calculate the stresses and energy release rates in delaminated orthotropic composite plates with Straight Crack Front. The delaminated parts are modeled by the general third-order plate theory, while a double-plate model with interface constraint is developed for the unCracked portion of the plate. The governing equations of the unCracked part are formulated by considering the equilibrium and the displacement continuity along the interface. As an example, a simply-supported delaminated orthotropic plate subjected to a point force is solved adopting Lévy plate formulation and the state-space approach. The mode-II and mode-III energy release rate distributions along the Crack Front were calculated by the J-integral. To verify the analytical results the 3D finite element model of the plate was constructed and the energy release rates were calculated by the virtual Crack-closure technique. A previous second-order plate theory solution was also utilized in the course of the comparison. The results indicate a good agreement between analysis and numerical computation and that third-order theory is better in some cases than the second-order approximation
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Sensitivity analysis for frequency based prediction of Crack size in composite plates with through-the-width delamination
International Journal of Damage Mechanics, 2017Co-Authors: Z. Juhász, Tamás Turcsán, Tamás Tóth, András SzekrényesAbstract:This work combines modal analysis measurements with a novel 2D finite element plate model, which is capable to determine the delamination growth based on the change in the measured frequencies. The base of the presented method is a finite element model incorporating the Classical Laminated Plate Theory, and it is capable to estimate the eigenfrequencies of a rectangular plate with through-the-width delamination and Straight Crack Front using arbitrary boundary conditions. The model contains special types of finite elements for modelling the delamination. This results a contact free model, which improves the simulation speed significantly. Using this model, the characteristic of the change of the eigenfrequencies with respect to the delamination growth can be obtained. These results can serve as reference, and according to the theoretical curves, the actual size of the delamination can be estimated based on the change in the measured frequencies. According to our measurement results, it can serve as a good...
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Progressive buckling of a simply supported delaminated orthotropic rectangular composite plate
International Journal of Solids and Structures, 2015Co-Authors: Z. Juhász, András SzekrényesAbstract:Abstract In this work we analyse the buckling process of composite plates with trough-the-width delamination and Straight Crack Front applying uniaxial compression. Local, global and mixed mode buckling cases are considered. The novel part of this work is that the distribution of the resulting in-plane forces is taken into account for the analysis of the buckling of the delaminated plate portions. For determining the behaviour of the delaminated plate with respect to the external compression, first an analytical method is given for determining the global critical loads. Second the local critical forces are determined using a finite element model. For this analysis a semi-discrete element was developed for the delaminated plate portions. The analysis was carried out using the method of harmonic balance because of the distribution of the in-plane forces along the delamination Front. The buckling process of the plate with respect to the axial compression is determined from a displacement controlled model.
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Estimation of Local Delamination Buckling in Orthotropic Composite Plates Using Kirchhoff Plate Finite Elements
Mathematical Problems in Engineering, 2015Co-Authors: Z. Juhász, András SzekrényesAbstract:We analyse the buckling process of composite plates with through-the-width delamination and Straight Crack Front applying uniaxial compression. We are focusing on the mixed mode buckling case, where the non-uniform distribution of the in-plane forces controls the occurence of the buckling of the delaminated layers. For the analysis, semi-discrete finite elements will be derived based on the Levy-type method. The method of harmonic balance is used for taking into account the force distribution that is generally non uniform in-plane.
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Estimation of Local Delamination Buckling in Orthotropic Composite Plates Using Kirchhoff Plate Finite Elements
Mathematical Problems in Engineering, 2015Co-Authors: Z. Juhász, András SzekrényesAbstract:© 2015 Zoltán Juhász and András Szekrényes.We analyse the buckling process of composite plates with through-the-width delamination and Straight Crack Front applying uniaxial compression. We are focusing on the mixed mode buckling case, where the non-uniform distribution of the in-plane forces controls the occurence of the buckling of the delaminated layers. For the analysis, semi-discrete finite elements will be derived based on the Lèvy-type method. The method of harmonic balance is used for taking into account the force distribution that is generally non uniform in-plane.
Z. Juhász - One of the best experts on this subject based on the ideXlab platform.
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Sensitivity analysis for frequency based prediction of Crack size in composite plates with through-the-width delamination
International Journal of Damage Mechanics, 2017Co-Authors: Z. Juhász, Tamás Turcsán, Tamás Tóth, András SzekrényesAbstract:This work combines modal analysis measurements with a novel 2D finite element plate model, which is capable to determine the delamination growth based on the change in the measured frequencies. The base of the presented method is a finite element model incorporating the Classical Laminated Plate Theory, and it is capable to estimate the eigenfrequencies of a rectangular plate with through-the-width delamination and Straight Crack Front using arbitrary boundary conditions. The model contains special types of finite elements for modelling the delamination. This results a contact free model, which improves the simulation speed significantly. Using this model, the characteristic of the change of the eigenfrequencies with respect to the delamination growth can be obtained. These results can serve as reference, and according to the theoretical curves, the actual size of the delamination can be estimated based on the change in the measured frequencies. According to our measurement results, it can serve as a good...
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Progressive buckling of a simply supported delaminated orthotropic rectangular composite plate
International Journal of Solids and Structures, 2015Co-Authors: Z. Juhász, András SzekrényesAbstract:Abstract In this work we analyse the buckling process of composite plates with trough-the-width delamination and Straight Crack Front applying uniaxial compression. Local, global and mixed mode buckling cases are considered. The novel part of this work is that the distribution of the resulting in-plane forces is taken into account for the analysis of the buckling of the delaminated plate portions. For determining the behaviour of the delaminated plate with respect to the external compression, first an analytical method is given for determining the global critical loads. Second the local critical forces are determined using a finite element model. For this analysis a semi-discrete element was developed for the delaminated plate portions. The analysis was carried out using the method of harmonic balance because of the distribution of the in-plane forces along the delamination Front. The buckling process of the plate with respect to the axial compression is determined from a displacement controlled model.
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Estimation of Local Delamination Buckling in Orthotropic Composite Plates Using Kirchhoff Plate Finite Elements
Mathematical Problems in Engineering, 2015Co-Authors: Z. Juhász, András SzekrényesAbstract:We analyse the buckling process of composite plates with through-the-width delamination and Straight Crack Front applying uniaxial compression. We are focusing on the mixed mode buckling case, where the non-uniform distribution of the in-plane forces controls the occurence of the buckling of the delaminated layers. For the analysis, semi-discrete finite elements will be derived based on the Levy-type method. The method of harmonic balance is used for taking into account the force distribution that is generally non uniform in-plane.
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Estimation of Local Delamination Buckling in Orthotropic Composite Plates Using Kirchhoff Plate Finite Elements
Mathematical Problems in Engineering, 2015Co-Authors: Z. Juhász, András SzekrényesAbstract:© 2015 Zoltán Juhász and András Szekrényes.We analyse the buckling process of composite plates with through-the-width delamination and Straight Crack Front applying uniaxial compression. We are focusing on the mixed mode buckling case, where the non-uniform distribution of the in-plane forces controls the occurence of the buckling of the delaminated layers. For the analysis, semi-discrete finite elements will be derived based on the Lèvy-type method. The method of harmonic balance is used for taking into account the force distribution that is generally non uniform in-plane.
James R. Rice - One of the best experts on this subject based on the ideXlab platform.
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Disordering of a dynamic planar Crack Front in a model elastic medium of randomly variable toughness
Journal of The Mechanics and Physics of Solids, 1994Co-Authors: Gilles Perrin, James R. RiceAbstract:Abstract Rice et al . (1994, J. Mech. Phys. Solids 42 , 813–843) analyse the propagation of a planar Crack with a nominally Straight Front in a model elastic solid with a single displacement component. Using the form of their results for a strictly linearized perturbation from a Straight Crack Front which moves at uniform speed, we give the corresponding first-order expression for the deviation of a Crack Front from Straightness as a direct integral expression in the deviation of the material toughness from uniformity in the Crack plane. We then use this expression to analyse the autocorrelation of the Crack Front position when the toughness deviations are random. We find that the root mean square deviation in position diverges logarithmically with travel distance across the random toughness region, as do the variances of the propagation velocity and slope of the Crack Front. That is, according to strictly linearized analysis, perturbed about the solution for a uniformly moving Crack Front, the perturbations from Straightness and from uniform propagation speed should grow without bound in the presence of random deviations in toughness. What is remarkable about this result is that, according to the same strictly linearized analysis, if the toughness is completely uniform over the remaining part of the fracture plane, after encounter with a region of nonuniform toughness, the moving Crack Front becomes asymptotically Straight with increase of time. Nonlinearities, not considered here, must control how statistically disordered the Crack Front can ultimately become as it propagates through a region of random toughness variation. Also, because of the logarithmic nature of the growth, significant disorder can occur in response to small perturbations only when the Crack moves over a great distance compared to the correlation length scale in the fracture toughness.
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Three-dimensional perturbation solution for a dynamic planar Crack moving unsteadily in a model elastic solid
Journal of The Mechanics and Physics of Solids, 1994Co-Authors: James R. Rice, Yehuda Ben-zionAbstract:A half-plane Crack propagates dynamically, nominally in the x direction, along the plane y = 0 in an unbounded solid subjected to remote loading equivalent to a static stress intensity factor K∗. The Crack Front at time t lies along the arc x = v0t + ϵƒ(z, t) where ƒv0 is a constant velocity, (z, t) is an arbitrary function, and ϵ is a small parameter. The Crack Front speed thus varies along the z axis and its shape deviates from Straightness. We address this problem within a model 3D elastodynamic theory involving a single displacement variable u, satisfying a scalar wave equation, and representing tensile opening or shear slippage, with associated tensile or shear stress σ = M δuδy across planes parallel to the Crack, where M is an elastic modulus. The problem is then one of finding a solution to the scalar wave equation satisfying σ = 0 on y = 0 within the rupture. When ϵ = 0 the solutions for u, σ, dynamic stress intensity factor K and energy release rate G are familiar 2D results. We develop corresponding 3D solutions to first order in σ, for arbitrary ƒ(z, t). The solutions are used to address in some elementary cases how a Crack Front moves unsteadily through regions of locally variable fracture resistance. When a Straight Crack Front approaches a slightly heterogeneous strip, lying parallel to the Crack tip along an otherwise homogeneous fracture plane, it may be blocked by asperities after some advancement into the heterogeneous region if it has a relatively small incoming velocity. If, however, the incoming Crack velocity is relatively high, the asperities give way and the, now curved, Crack Front propagates into the bordering homogeneous region. There, the moving Crack Front recovers a Straight configuration through slowly damped space-time oscillations. The oscillatory Crack tip motion results from constructive-destructive interferences of stress intensity waves, initiated by encounters of the Crack Front with asperities, and then propagating along the Front. Oscillations in response to a heterogeneity that is spatially periodic in the direction along the Crack Front decay as tt-12 at large t. The slowness of the decay suggests that the Straight Crack Front configuration may be sensitive to small sustained heterogeneity of the fracture resistance. This is consistent with results of a related analysis (Perrin and Rice, 1994, in press, J. Mech. Phys. Solids) based upon a strictly linearized form of our equations. The persistence of unsteady Crack tip motion beyond the immediate region of heterogeneities provides an explanation for high frequency seismic radiation, using a lesser amount of heterogeneity than what might be naively assumed by strict correspondence of all curved and variable velocity portions of a propagating rupture Front to asperities. Also, oscillations of Crack tip velocity in the presence of sustained small heterogeneities, suggested by features of our 3D results for the model theory, may provide a mechanism for the generation of rough tensile fracture surfaces when the average (macroscopic) propagation speed of the Crack is relatively small.
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Penetration of a Quasi-statically Slipping Crack Into a Seismogenic Zone of Heterogeneous Fracture Resistance
Journal of Geophysical Research, 1991Co-Authors: James R. RiceAbstract:This paper is concerned with some aspects of nonuniform stressing above a deep creeping portion of a fault zone prior to a large crust-breaking earthquake. The model that we use involves a slipping Crack, representing the deeper, more stably sliding portions of the fault zone, which penetrates upward from depth and is blocked in the lower region of the seismogenic zone. When conditions are uniform along strike, the upward penetration at the Crack Front is by mode III in strike-slip fault zones but by mode II in thrust or normal fault zones. Two major results are reported. First, we analyze approximately, via a linear perturbation formulation, how a tectonic Crack Front encounters and ultimately shears through arrays of localized “asperities” that are distributed parallel to the Crack Front and have a toughness which is greater than that of adjoining segments of the fault zone. Using a fast Fourier transform based numerical procedure to simulate Crack penetration into asperities, we find a notable difference between mode II and mode III Crack Fronts in that the former penetrates approximately twice as far between the asperities as the latter under the same loading level. This is interesting because observations of slip distribution in large earthquakes suggest that there is a significant aseismic component to the total slip budget in subduction zone earthquakes, which in contrast does not seem to be present in strike-slip zone earthquakes, and also that the surface slip distribution in continental dip-slip faulting is typically much more irregular than for strike-slip faulting. In a simulation involving multiple rows of periodic asperities we note that the more deeply penetrating mode II Crack Front contacts more asperities simultaneously while breaking them at different load levels compared to the less flexible mode III Crack Front, which simply breaks one row of asperities and jumps (unstably) to the next. The second major result concerns whether a Straight Crack Front in the lithosphere along a strike-slip fault zone is configurationally stable, that is, whether the Crack Front will tend to remain Straight as the Crack penetrates upward from depth. It is found that for infinitesimal perturbations of the Straight Front beyond a critical wavelength, of the order of the crustal lithosphere thickness, the stress intensity factor is higher at the most advanced portions of the Crack Front rather than at the least advanced; the opposite is true at shorter wavelengths. When resistance to Crack growth is essentially uniform over the fault plane, this means that the Straight Crack Front is configurationally unstable at long wavelengths. The issue of configurational stability is related to the concept of fault segmentation, which is based on the observation that fault zones, particularly long ones, do not rupture along their entire length during a single earthquake. Effect of a vertical gradient of fracture resistance is discussed in the appendix, where it is shown that a significant upward gradient of resistance to Crack growth may completely stabilize the Straight Crack configuration.
V. Vitek - One of the best experts on this subject based on the ideXlab platform.
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Significance of the deviations of the Crack Front into the plane perpendicular to the Crack propagation direction - I. Crack-Front dislocation generation
International Journal of Fracture, 2003Co-Authors: P.n.b. Anongba, V. VitekAbstract:A static Crack Front deviates more and more from Straight line in a solid as I. the number of dislocations generated from the Crack Front increases and/or II. the temperature increases. The significance of these deviations into the plane perpendicular to the Crack propagation direction is the subject of the present study, which we divide into two parts. In this paper (Part I), the influence of dislocation generation on the shape of a static Crack Front and on the conditions for Crack motion are investigated. We have considered an elastic-plastic Crack model in which, due to dislocation generation during mode I loading, the initially Straight Crack Front deviates in the sinusoidal form in a plane perpendicular to both the average Crack plane and the direction of fracture propagation. No Crack opening displacement is allowed. The dislocations generated form a plastic zone separated from the Crack by a dislocation free zone. Both the Crack and the plastic zone are described in terms of continuous distributions of dislocations that are sinusoidal and Straight edges, respectively. Expressions for the dislocation distributions, the relative displacement of the faces of the Crack, the number of dislocations in the plastic region, and the Crack opening force G per unit length of the Crack Front are evaluated. The similarities with isolated Cracks (planar and wavy) are emphasized. It is shown that the stress at the Front of the sinusoidal Crack is unbounded in the mean fracture plane but bounded outside. Consequently, only the Crack Front sites located on the average Crack plane are possible sites for the initiation of Crack motion. G differs from that of the planar Crack by a geometrical factor that depends on a new parameter, the Crack Front inclination angle θ. This is an acute angle, measured in the plane perpendicular to the Crack propagation direction, between the Crack Front and the average fracture plane. As θ increases with the number of dislocations generated, G decreases and is ultimately zero for a critical value θ_c= tan ^−1(1/ sqrt ν) where ν is the Poisson ratio. This is a new condition for Crack arrest in solids. Applying the theory to a steel, it is found that this condition could be achieved under localized plastic yielding at Crack tips.
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Significance of the deviations of the Crack Front into the plane perpendicular to the Crack propagation direction - I. Crack-Front dislocation generation
International Journal of Fracture, 2003Co-Authors: P.n.b. Anongba, V. VitekAbstract:A static Crack Front deviates more and more from Straight line in a solid as I. the number of dislocations generated from the Crack Front increases and/or II. the temperature increases. The significance of these deviations into the plane perpendicular to the Crack propagation direction is the subject of the present study, which we divide into two parts. In this paper (Part I), the influence of dislocation generation on the shape of a static Crack Front and on the conditions for Crack motion are investigated. We have considered an elastic-plastic Crack model in which, due to dislocation generation during mode I loading, the initially Straight Crack Front deviates in the sinusoidal form in a plane perpendicular to both the average Crack plane and the direction of fracture propagation. No Crack opening displacement is allowed. The dislocations generated form a plastic zone separated from the Crack by a dislocation free zone. Both the Crack and the plastic zone are described in terms of continuous distributions of dislocations that are sinusoidal and Straight edges, respectively. Expressions for the dislocation distributions, the relative displacement of the faces of the Crack, the number of dislocations in the plastic region, and the Crack opening force G per unit length of the Crack Front are evaluated. The similarities with isolated Cracks (planar and wavy) are emphasized. It is shown that the stress at the Front of the sinusoidal Crack is unbounded in the mean fracture plane but bounded outside. Consequently, only the Crack Front sites located on the average Crack plane are possible sites for the initiation of Crack motion. G differs from that of the planar Crack by a geometrical factor that depends on a new parameter, the Crack Front inclination angle θ. This is an acute angle, measured in the plane perpendicular to the Crack propagation direction, between the Crack Front and the average fracture plane. As θ increases with the number of dislocations generated, G decreases and is ultimately zero for a critical value θc=tan−1(1/sqrtν) where ν is the Poisson ratio. This is a new condition for Crack arrest in solids. Applying the theory to a steel, it is found that this condition could be achieved under localized plastic yielding at Crack tips.
Jean Petit - One of the best experts on this subject based on the ideXlab platform.
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Three-dimensional modeling of plasticity-induced Crack closure in a 304L stainless steel: influence of Crack length and Crack shape
2013Co-Authors: Catherine Gardin, Christine Sarrazin-baudoux, Mandana Arzaghi, Jean PetitAbstract:This paper addresses a precise investigation of the behaviour of physically short 2D Cracks in condition where LEFM concepts are applicable. The influence of the plasticity-induced Crack closure (PICC) on the global and local effective stress intensity factor is particularly investigated and modelled under constant K amplitude loading in order to avoid any influence of loading history. Three-dimensional numerical models under Abaqus were used to determine the opening kinematics and to model the influence of Crack length in the case of 2D through Cracks with a Straight Crack Front or a curved Crack Front. Introduction The concept of Crack closure, consisting in a premature contact of the Crack lips during cyclic loading, as initially proposed by Elber [1] is widely used to rationalize the propagation curves and has become one of the most intensively studied phenomena associated with fatigue Crack growth. The closed Crack is considered as non-effective for Crack propagation. Therefore, the effective Keff (near tip) stress intensity factor range has been introduced to describe the effective driving force for Crack propagation in condition of mode I Crack opening. Consequently, characterization of closure has been intensively studied for long Cracks. The higher Crack growth rate of short Cracks as compared to long Cracks has been related in several cases to the lack of significant closure because of a small Crack wake around Crack lips [2-4]. When the LEFM conditions are satisfied, closure of short Cracks has been shown to increase when Cracks propagate, finally reaching the behaviour of long Cracks [5, 6]. Suresh and Ritchie [3] suggested the following definitions by which short Cracks can be broadly classified: i) Crack whose size is comparable to the scale of the characteristic microstructural dimension is referred as microstructurally small Cracks; ii) Cracks for which the near-tip plasticity is comparable to the Crack size are referred as mechanically small Cracks; iii) fatigue flaws significantly larger than the characteristic microstructural dimension and the scale of the local plasticity are referred as physically short Crack. Physically short Cracks with initial dimensions larger than 3 to 5 times the average grain size, and when “far field” loading conditions allow the application of the linear fracture mechanic parameters, are relevant to the third type of this classification. This is the case of the Cracks presently considered. The plasticity-induced Crack closure (PICC) induced by constant stress intensity factor ranges is studied in a 304L stainless steel that undergoes high plasticity [7]. Three-dimensional simulations with both Straight (for reasons of computing time) and circular curved Fronts (for a better approximation of experimental observations of the real Crack curvature) have been done to describe the influence of the length of 2D physically short Cracks on the contribution of Crack closure on the effective driving force. Geometry of the model The geometry modelled in this work corresponds to a CT-50 Compact Tension specimen with a thickness B=10mm, subjected to mode I loading. The analytical expression of the stress intensity factor is the following [8]: W B Y F K with 2 / 3 4 3 2 / 1 / 6 . 5 / 72 . 14 / 31 . 13 / 64 . 4 886 . 0 / 2 W a W a W a W a W a W a Y (1) where F is the applied load, a is the Crack length. Here, w=50mm. Whatever the shape of the Crack considered here, we will calculate K by using the edge Crack length, as it is the one measured during tests via optical observations. For symmetry reasons, only a quarter of the CT specimen has been modelled. We impose here constant values of the stress intensity factor amplitude K, with a stress ratio R=0.1. The load is imposed by applying cyclic pressure on a quarter of the two holes of the CT specimen. We have used cubic linear elements, as generally used in 3D modelling [9, 10]. As important gradients of stresses and strains appear in the vicinity of the Crack tip, the choice of element type and size of mesh is crucial, in order to obtain accurate results in a reasonable calculation time. The size of the elements should permit a precise characterization of the monotonic and plastic Rp zones. The minimum size proposed by Dougherty [11] is the following:
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Wake length and loading history effects on Crack closure of through-thickness long and short Cracks in 304L: Part II - 3D numerical simulation
Engineering Fracture Mechanics, 2013Co-Authors: Catherine Gardin, Christine Sarrazin-baudoux, Jean PetitAbstract:The plasticity-induced Crack closure shielding effect for long and short through-thickness Cracks is studied in a 304L steel. A main objective is to uncouple the effect of the wake length from that of the wake history. The experimental results are presented in a first part of this contribution. In the present second part, a 3D finite elements analysis (ABAQUS) for 2D Cracks with a Straight Crack Front is proposed. Globally, a remarkable consistence is obtained between simulation and experiments. The effective stress intensity factor range is confirmed as the driving force when the LEFM concepts are applicable.