Transverse Crack Tip Research Articles

Effect of heat treatment processes on hydrogen embrittlement in hot-rolled medium Mn steels

The influence of heat treatment processes, which consist of a quenching partitioning (QP) process, intercritical annealing (IA) process and warm rolling (WR) process, on the hydrogen embrittlement (HE) of medium Mn steels is investigated. The corresponding experimental specimens are labeled QP160, IA810 and WR760, respectively. WR760 reveals the best mechanical properties, and the corresponding product strength and elongation (PSE) is 42.9 GPa•%; nevertheless, HE susceptibility is the lowest due to fine grains and microcrack propagation paths, which are parallel to rolling direction (RD), and they relax the triaxial stress conditions ahead of the main transverse crack's tip. IA810 (PSE = 29.1 GPa•%) shows the highest HE susceptibility due to the extremely unstable γ, which makes the microcrack propagation along the interface of γ(α′)/α-ferrite occur more easily when there is hydrogen. Compared to IA810, QP160 (PSE = 17.6 GPa•%) reveals a lower HE susceptibility due to the higher γ stability.

A variational approach for predicting initiation of matrix cracking and induced delamination in symmetric composite laminates under in-plane loading

Abstract This paper discusses the formation of matrix cracking and induced delaminations in a [ ϕ m ( 2 ) / ψ n ( 1 ) ] s $[\phi _m^{(2)}/\psi _n^{(1)}]s$ laminate subject to arbitrary in-plane loading using a variational approach. To this end, the effects of delaminations coming from the tips of transverse cracks in the middle sublaminates are considered to specify the critical crack density points and finally understand which modes of damage are prospects for various lay-ups in the presence of transverse cracks as well as induced delamination. After deriving a very good approximation of the principle of minimum complementary energy by considering complex equations, the stress fields are provided. In this analysis, a unit cell in the ply level of a composite laminate containing both matrix cracking and delamination is considered. Then, the values of the admissible stresses and compliance of cracked laminate are employed to evaluate the energy release rate of each mentioned damage mode. Eventually, the graphs for different lay-ups in such symmetric laminate are drawn, which indicate important points for designers in practical applications. Afterwards, the effects of thickness on the dislocation of critical crack density points are checked. It can be emphasized that the current approach opens a new insight for perceiving the composites’ structural behavior in vulnerable positions.

ENERGY-BASED ANALYSIS OF TRANSVERSE CRACKING AND INDUCED DELAMINATION IN [S'/90n/S]s LAMINATES: A VARIATIONAL APPROACH

Analysis of transverse-ply cracking and small delaminations emanating from the tips of transverse cracks is extended to symmetric laminates having more general layup configurations. Almost all studies on induced delamination due to transverse-ply cracking are limited to [S/90n]s laminates, where (S) is any orthotropic sublaminate that is much stiffer than [90n]. In this paper, the evolution of transverse matrix cracking and the induced delamination from it is investigated for laminates with more general layups [S'/90n/S]s. In this configuration, the cracked layer is offset to the midplane of the laminate and is constrained by the two orthotropic sublayers. The micromechanics-based model is developed using a variational approach to find the stress field of a unit-cell in a generalized plane strain condition. A combined analytical/numerical methodology is used to solve the boundary value problem. The total complementary potential energy of the unit-cell is calculated, as is the energy release rate for transverse cracking and induced delamination damage. The calculated energy release rate as a function of crack density and delamination length is obtained for different layup configurations, and in some cases the results are compared with results from the literature. Because the distribution of cracks in a structure is uniform, the results for the unit cell scale can be used for the structural scale.

Secondary damage effect on stress redistribution in laminated composites

Intralaminar matrix cracking is recognized as the primary mode of damage appearing in laminates. Local Raman strain measurements in neighboring layers show that the distribution shape in the vicinity of the crack tip is smoothened with increasing magnitude of the applied strain. This behavior is attributed to secondary damage development in the neighboring supporting plies close to the transverse crack tip. In this article, an approximate analytical variational model, based on the principle of minimum complementary energy, is proposed for the investigation of the stress state in a glass/ epoxy cross-ply laminate with cracks in 90°layer and with homogenized damage (reduced elastic properties) in part of the 0° layer. The extent of damage (fiber breaks) is estimated combining modeling with measured local strain distributions. The model is applied in order to examine the effect of ply thickness on the magnitude of the secondary damage at the transverse crack tip.

407 Cross-Ply CFRP積層板の高サイクル疲労におけるトランスバースクラック及び層間はく離進展挙動の調査(高分子/高分子基複合材料1)

Damage growth behavior of transverse crack and delamination in cyclic loading was studied with cross-ply laminates of carbon fiber reinforced plastics (CFRPs) composite. Damage of the specimens during the fatigue test was observed by soft X-ray photography. It was found that delamination growth behavior depended on the inter-laminer stress and the out-plane stress in thickness direction caused by free-edge effect. Quasi-isotropic, [45/0/-45/90]_s, laminates, are applied large peering stress at free edges of the specimen when the specimen is subjected to tensile stress. Therefore they showed edge delamination. On the other hands, cross-ply, [0/90_6]_s laminates, are applied large inter-laminer shear stress at transverse crack tips, and show local delamination originated by a transverse crack. Under the high-cycle loading, it was observed that depending on the applied stress level delamination growth behavior differed.

Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: Static and fatigue loading

A review of developments and understanding of transverse cracking and delamination in cross-ply laminates is presented. First, experimental investigations reported in the literature for analyzing the development of transverse cracking are considered. Next, characteristics of different models for evaluating the stress distribution in the damaged laminates are developed. It is shown how these models associated with the statistical description of strength or energy released in the 90° plies make it possible to describe the development of transverse cracking in monotonic or fatigue loading. According to the nature of cross-ply laminates, transverse cracking is not, however, sufficient for describing the development of transverse cracks in 90° plies in the case of monotonic loading. In this case, the delamination process induced at transverse crack tips is to be considered for describing the experimental results. There are 108 references in this review article.

トランスバースクラックを有するＣＦＲＰ直交積層板の引張強度

The effect of the transverse crack on the ultimate tensile strength (UTS) for carbon fiber reinforced plastic (CFRP) cross-ply laminates was studied experimentally and analytically. For various stacking sequences of CFRP composites, quasi-static tensile tests were carried out. And the fiber bundle strength of 0-degree ply was almost constant. Therefore, it was concluded that there was little notch sensibility in spite of the existence of transverse cracks. A new numerical model based on the finite element method was proposed to investigate the inner micro damage process. In the model the elastoplastic relation of epoxy matrix was considered effectively and the progress of the inner fiber breakage was obtained. Then, using this model, we conducted the simulation based on the Monte-Carlo method. Based on the analysis results of the proposed model, it was shown that the plastic regions at the tip of transverse crack reduce the concentration of stress, and the bundle strength was not affected by the existence of transverse cracks.

Vibrations of sandwich panels and beams with matrix cracks in the facings

The paper presents the solution of the vibration problem for sandwich panels and beams with matrix cracks in transverse layers of cross-ply facings. The closed-form solution is obtained by assumption that the panels can be characterized by the first-order shear deformation theory. The analysis accounts for a difference in the response of the facings with open and closed matrix cracks. Extension of the solution to the case of multi-skin panels is also discussed in the paper. In addition, the problem of vibration of sandwich beams with matrix cracks in the transverse layers and delaminations generating from the tips of transverse cracks is considered. As shown in this paper, although the presence of delaminations results in a larger reduction of the stiffness and free vibration frequencies than transverse cracking by itself, the changes in the frequencies remain relatively small.

Damage mechanics characterization of transverse cracking behavior in high-temperature CFRP laminates

Transverse cracking under tensile loading in high-temperature CFRP, carbon/BMI (bismaleimide), G40-800/5260, has been investigated experimentally. Carbon/epoxy, T800H/3900-2, composite laminates are also examined for comparison. Both material systems have toughened-interlaminar layers. Laminate configurations are [0/90]s, [0/902]s, [±45/90]s and [±45/902]s for G40-800/5260, while [0/90]s and [±45/90]s for T800H/3900-2. In all laminates, the first microscopic damage observed is a 90° ply transverse crack. In [±45/90n]s type laminates, cracking in 45°ply and delaminations are also observed. The cracking behavior is quantified by measuring crack densities as a function of the laminate strain. The difference between the damage progress near the 90° ply transverse crack tips between the material systems are observed. Damage mechanics analysis is used to predict 90° ply transverse cracking based on both the energy and stress criteria. The present analysis can be used as a means of characterization of the transverse cracking resistance of a material, which will be helpful in ranking materials.

A model for transverse cracking and delamination in cross-ply laminates

This paper develops an analytical model to evaluate the stress distibutions in cross-ply laminates subjected to tensile loading and containing transverse cracks and delamination initiated from the transverse crack tips. In the delaminated part the analytical approach is reduced to the usual one-dimensional analysis. In the part without delamination the analytical model is based on a displacement approach which considers that the longitudinal displacement depends on the longitudinal and transverse coordinates in each layer. The stress distributions derived from the analytical model are compared with the results obtained from a finite-element analysis.

The effect of delaminations induced by transverse cracks and splits on stiffness properties of composite laminates

In an effort to evaluate stiffness degradation due to delaminations growing at the 0°/90° interface from the tips of transverse cracks in the 90° plies and splits in the 0° plies of cross-ply [0 m /90 n ] s laminates, a new theoretical approach was developed. It employs the Equivalent Constraint Model of the damaged lamina [Fan J, Zhang J. In-situ damage evolution and micro/macro transition for laminated composites. Composites Science and Technology 1993;47:107–118], which allows one to avoid cumbersome consideration of the repeated laminate element defined by the intersecting pairs of transverse cracks and splits. It also uses an improved 2D shear-lag analysis [Zhang J, Soutis C, Fan J. Strain energy release rate associated with local delamination in cracked composite laminates. Composites 1994;25(9):851–862] to determine the stress fields in the explicitly damaged lamina and the In situ Damage Effective Functions to describe its reduced stiffness properties. Reduced stiffness properties of the damaged lamina are found to depend explicitly upon the crack density and relative delamination area associated with that lamina and implicitly upon two damage parameters associated with the neighbouring lamina. Theoretical predictions reveal that transverse crack tip delaminations cause significant reduction in the shear modulus and Poisson's ratio of cross-ply and symmetric balanced [± θ m /90 n ] s laminates. Dependence of the laminate reduced elastic properties on the orientation angle of the constraining ply is examined. Contribution of each damage mode (transverse cracking, transverse crack tip delaminations, splitting and split tip delaminations) into stiffness loss is established.

Delamination Originating from Transverse Crack Tips in Laminates under Mechanical Loadings

A singular finite element method is formulated utilizing the asymptotic solutions for displacements and stresses near the tip of interfacial crack between dissimilar anisotropic materials and the variational principle of a hybrid functional. Laminates with delamination originating from transverse crack tips are analyzed by the singular hybrid element at the delamination tip together with the conventional displacement-based elements around the hybrid element. Numerical results show the efficiency and accuracy of the present singular finite element for the analysis of the stress distributions near the tip of delamination in laminate under plane strain extension, antiplane shear and plane strain bending.

A Study of Matrix Crack Tip Delaminations and their Influence on Composite Laminate Stiffness

Reduction of the stiffness properties of cross-ply [0m/90n]s laminates due to delaminations, growing at the 0/90 interface from the tips of transverse cracks in the 90° plies and splits in the 0° plies, is analysed by means of a theoretical approach based on the Equivalent Constraint Model (ECM). Reduced stiffness properties of the damaged lamina are derived as explicit functions of the crack density and relative delamination area associated with that lamina and implicit functions of the two damage parameters associated with the neighbouring laminae. Transverse crack tip delaminations are found to cause significant reduction in the laminate shear modulus and Poisson's ratio. Contribution of each damage mode (transverse cracking, transverse crack tip delaminations, splitting and split tip delaminations) into stiffness loss is established.

Delamination originating from transverse crack tips in laminates under mechanical loadings

A singular finite element method is formulated utilizing the asymptotic solutions for displacements and stresses near the tip of the interface crack between dissimilar anisotropic materials and the variational principle of a hybrid functional. The interfacial crack problem can be analyzed by the singular hybrid element at the interfacial crack tip and the conventional displacement-based elements surrounding the crack element. Analyzing a small central interfacial crack between two large anisotropic composite layers with different fiber orientations subjected to uniform tensile load, we demonstrate that the present numerical solutions are in good agreement with the analytical ones for an interfacial crack between two semi-infinite anisotropic solids. Then, we apply the present method for the analysis of delamination originating from the transverse crack tip in laminates under plane strain extension, antiplane shear and plane strain bending.

Micromechanical characterization of local deformation in interlaminar-toughened CFRP laminates

The in situ SEM micro-line/grid methods were applied for quantitative evaluation of microscopic deformation in interlaminar-toughened CFRP cross-ply laminates with transverse cracks. Both the local deformation in the interlaminar region around the transverse crack tip and the crack opening displacement (COD) were observed at different temperatures to evaluate the effect of thermal residual stress. A two-dimensional approximate elastic analysis of stress and displacement fields in interlaminar-toughened cross-ply laminates with transverse cracks was conducted and compared with the experimental results. A reasonable agreement was obtained which implied the applicability of the analysis. The analysis will be a basis for the optimal design of interlaminar-toughened composite laminates.

Application of microline/grid methods to temperature dependent microscopic deformation and damage in CFRP laminates

Tensile tests of CFRP symmetric cross-ply laminates are carried out in a scanning electron microscope (SEM), and microscopic interlaminar deformation and damage near the transverse crack tip are visualized by microlines or microgrids printed on the specimen edge surface. The local deformation around the transverse crack tip is observed at 20°C, 80°C, 120°C and 160°C to evaluate the effect of thermal residual stress on the microscopic deformation and damage in the interlaminar region near the transverse crack tip. Temperature dependence of the axial crack opening displacement (COD) is also measured. The displacement field of the specimen edge surface obtained from these experimental results is compared with the theoretical model proposed by Lee, Allen and Harris. The analysis is modified to consider the temperature effect, and a good agreement is obtained between the modified theoretical predictions and experimental results.

Stress-strain state near a straight-through transverse crack tip in a special multi-sheet plate structure

The elastic stress-strain state of a multi-sheet structure with a straight-through transverse curvilinear crack is under investigation. The structure is made up of several plates and is loaded so that in each of its sheets the stress intensity near the crack tip is a function of four rather than two linearly non-interdependent factors, owing to which the structure with a crack under study differs fundamentally from a single plate with a crack. Asymptotic representations of the stresses and displacement components near the crack tip are given. Also, analytical expressions for the invariant Rice-Cherepanov integrals are given.

Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/902]s, [02/902]s and [02/904]s graphite/epoxy cross-ply laminates: good agreements are obtained.

A transverse crack tip field in bimaterial

The asymptotic field near an interface crack tip is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed.

Initiation and growth of delamination from the tips of transverse cracks in CFRP cross-ply laminates

Delamination initiation and growth from the tips of the transverse cracks in toughened-type CFRP (T800H/3631) cross-ply laminates was measured by the replica technique as a function of the applied laminate strain. In addition, loading/unloading tests were performed to obtain the relationship between the measured material damage and Young's modulus reduction. ENF (end-notched flexure) tests were also performed to obtain the mode II interlaminar fracture toughness in order to understand the delamination growth behavior. A simple shear-lag stress analysis was extended to the laminates containing delaminations at the tips of transverse cracks. This stress analysis was used to obtain Young's modulus reduction and the energy release rate associated with the delamination growth. The shear-lag prediction of Young's modulus reduction was compared with experimental data. The total delamination length was predicted as a function of the applied laminate strain by using the energy release rate and the experimentally obtained mode II interlaminar fracture toughness.