Influence of in-plane fibre orientation on mode I interlaminar fracture toughness of stitched glass/polyester composites

The influence of in-plane fibre orientation on the mode I interlaminar fracture toughness, G_Ic of unstitched and stitched glass/polyester composites is investigated in this paper. The G_Ic of planar specimens depends on the fibre orientation, θ in the layers adjacent to the fracture plane, in addition to the property of matrix material. The mode I fracture toughness and fracture behavior of unstitched and stitched 0/0, 30/−30, 45/−45, 60/−60, 90/90 and 0/90 interfaces of unidirectional fibre mats (UD) and 30/−30, 45/−45 and 90/90 interfaces of woven roving mats (WRM) are studied. WRM layer orientation is represented by the direction of warp fibres. Stitching is done by untwisted Kevlar fibre roving of Tex 175 g/km at the stitch densities (number of stitches per unit area) of 10.24 and 20.48 stitches/inch². The specimens having same stitch density, but different stitch distributions are prepared, and the influence of stitch distribution on G_Ic is studied. Double cantilever beam (DCB) tests are carried out and the G_Ic is determined using modified beam theory. The G_Ic of both unstitched and stitched specimens increases with increase in orientation angle, θ upto 45° above which it decreases. The G_Ic values of unstitched 45/−45 delamination interface is around 2.4 times that of the unstitched 0/0 interfaces. The influence of fibre orientation on G_Ic is clearly observed in unstitched specimens, whereas in the stitched specimens, stitching plays an important role in improving the G_Ic and suppresses the influence of fibre orientation; degree of suppression increases with increasing stitch density. When the value of θ is above 45°, transverse cracks are observed in the delamination interface surrounded by UD layers; while in the delamination interface surrounded by WRM layers, transverse cracks are not initiated irrespective of the fibre orientation angle.     

Double cantilever beam testing of multidirectional laminates

Several difficulties in the double cantilever beam (DCB) tests of multidirectional laminates often prevent valid measurements of the mode I critical strain energy release rate G_Ic. In this paper, several DCB specimens were analysed with 3D finite element models. The results showed that the undesired effects of residual stresses and of mode-mixity can be minimised. An interlaminar stress based fracture criterion predicts that the G_Ic of multidirectional specimens is typically 10–40% higher than the G_Ic of unidirectional [0°]_n laminates. This agrees with the few valid experimental data available.     

Mechanics and mechanisms of delamination in a poly(ether sulphone)—Fibre composite

The interlaminar fracture behaviour of AS4/PES (poly(ether sulphone)) composite has been investigated in Mode I, Mode II and for fixed Mode I to Mode II ratios of 0·84, 1·33 and 2·13. The data obtained from these tests have been analysed using several different analytical approaches. The results obtained show that in Mode I the interlaminar crack growth in double cantilever beam (DCB) specimens is accompanied by fibre bridging behind the crack tip and by splitting at the crack tip, and in Mode II by the formation of a damage zone at the crack tip. These failure mechanisms are shown to increase the value of the interlaminar fracture energy considerably as the crack propagates through the composite, i.e. a rising ‘R-curve’ is measured. It is shown also that the value of the interlaminar fracture energy at crack initiation in Mode I, G_CI (init), increases as the length of the initial precrack is increased. The lowest G_IC (init) value obtained for the poly(ether sulphone) (PES) composite in this study is 0·8 kJm⁻², and this value was ascertained from a specimen with the precrack being grown by about 2 mm ahead of the initial crack (a₀ = 23 mm, a_p = 25 mm). The typical Mode II steady-state propagation energy, G_IIC (s/s-prop), value obtained for the specimens was about 2·0 kJm⁻². The length of the initial precrack had no significant effect on the G_IIC (init) and G_I/IIC (init) values. The Mode II tests gave values of G_IIC (init) = 1·25 kJm⁻² and of G_IIC (s/s-prop) = 1·85 kJm⁻². Finally, the failure loci for the PES composite have been constructed and theoretical expressions to describe these data considered.     

Contributions of internal hydrogen and room-temperature creep to the abnormal fatigue cracking of Ti6246 at high Kmax

This study aims at explaining the absence of a threshold for crack propagation in an /β titanium alloy during cyclic tests performed with constant K_max and increasing K_min, if K_max is higher than 60–70% of K_Ic. Tensile, creep as well as fatigue crack growth tests are performed on specimens with various hydrogen content. SIMS analyses of hydrogen content around the tip of a crack developed in the abnormal regime are made. Solute hydrogen is shown to segregate at the crack tip and to enhance room-temperature creep, strain localisation and decohesion along /β interfaces.     

Recent considerations in experimental compliance calibration of the WOL specimen

This report summarizes work directed at the verification of currently used compliance relationships for the wedge-open-loading (WOL) specimen geometry frequently used in fatigue crack propagation testing. An overview is given of compliance curve fitting procedures. A new procedure is proposed which appears to offer significant advantages. Extensive testing and analytical details are included so that compliance procedures for crack growth monitoring can be improved. Compliance calibration results are presented for Ti-6Al-4V(RA) and Ti-6Al-4V(β) alloys.

Analytical procedures for obtaining the stress intensity calibration function (C₃) from experimental compliance results were compared and the proposed three parameter fit was found to be superior. The advantages of this proposed data analysis procedure are: small numbers of constants; relationship between normalized compliance (compliance × modulus × thickness) and normalized crack length (crack length/specimen width) is differentiable and invertible; consistency with physical reasoning; and discussion of possible differences in compliance due to material differences can be restricted to a single parameter.

For Ti-6Al-4V(β), the experimentally based C₃ values were found to be similar to analytically derived values, while for Ti-6Al-4V(RA) they differed significantly. Possibly this difference in RA results was due to the highly textured material used for the experimental investigation.     

Analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam specimen using higher order beam theories

Mathematical models, for the stress analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam (DCB) specimen using classical beam theory, first and higher order shear deformation beam theories, have been developed to determine the mode I strain energy release rate (SERR) for unidirectional composites. In the present study, appropriate matching conditions at the crack tip of the DCB specimen have been derived by using variational principles. SERR has been calculated using compliance method. In general, the performance of shear deformation beam models of DCB specimen with variationally derived matching conditions at the crack tip is good in determining the SERR for medium to long crack lengths. Performance of higher order shear deformation beam model (having quadratically varying transverse displacement over the thickness) of DCB specimen, with non-variationally derived matching conditions at the crack tip, is good in determining the SERR for all the crack lengths in comparison with the available theoretical and finite element solutions in the literature. Higher order shear deformation beam theories having varying transverse displacement over the thickness are more appropriate to analyze DCB specimen as they predict the appropriate nature of the interlaminar normal stress at the crack tip and its distribution ahead of the crack tip.     

圆弧形单向纤维增强树脂复合材料的I型层间断裂韧性测试及分析

层合板的I型层间断裂韧性的测量方法通常为单向纤维增强树脂复合材料的末端切口(End notched flexure, ENF)试样的双悬臂梁(Double cantilever beam, DCB)试验。为了得到带有弧度的层合复合材料结构的I型层间断裂韧性,对圆弧形末端切口(Arc-ENF)试样进行DCB试验。基于梁的弯曲理论和Irwin-Kies公式得到Arc-ENF试样的柔度公式与I型临界能量释放率G_IC公式,并且利用ABAQUS软件对DCB试验进行数值模拟。最终,通过对比分析理论公式计算结果、数值模拟结果和DCB试验结果来验证柔度公式和G_IC公式的合理性和有效性,对带有任意弧度的DCB试样的I型层间断裂韧性的测试与分析具有参考价值。      

Quasi-static fracture toughness testing of a single CT specimen at two test conditions

Abstract

It is proposed that a single CT specimen can be used for determining J ₀.₂ at two testing conditions, provided it can be ensured that the crack tip plastic zones for the two tests do not interfere. This is achieved by extending the crack at the end of the first fracture test by fatigue cycling at ambient temperature to obtain the starting crack for the second test. This method has been validated by testing thermally aged CT specimens of modified 9Cr - 1Mo steel at 653 K and 803 K. The J-Δa values obtained by a multispecimen method at a specific temperature were on a single curve irrespective of whether the data were generated from the first test or second test on that sample. Also, the J-Δa curves obtained using a single specimen normalisation method from data on first and second tests were within the expected specimen to specimen variation.     

Hardness, internal stress and fracture toughness of epitaxial AlxGa1−xAs films

Vickers microhardness indentations of 10 μm (001) oriented epilayers of Al_xGa_1−xAs on GaAs substrates have been utilized to evaluate the hardness H_v, the internal stress, and the fracture toughness K_Ic of the layers as a function of their composition parameter x. The hardness H_v varies linearly according to: (6.9-2.2x) GPa and K_Ic increases linearly with x according to: K_1c = (0.44+1.30x) MPa m^1/2. The influence of the substrate on these measurements was found to be negligible for the layer thickness (10 μm) and the indentation load (0.25 N) used, disregarding internal stresses.

Internal film stresses were evaluated by the bimorph buckling method, and were found to depend on the composition parameter according to σ = 0.13x GPa. These stresses did not notably affect the H_v measurements, but for K_Ic corrections as large as 25% had to be made.

The radial cracks observed were of the shallow Palmqvist type. In contradiction to previous reports on this type of cracking, it was found to initiate during unloading, not during loading, and a physical explanation for this deviation is given. No deep radial/median cracks were observed. It was found important to use expressions based on the correct crack geometry in the K_Ic evaluation. Also, a simple theory for the influence of internal stresses on the K_Ic results has been developed.     

Analysis of the sandwich DCB specimen for debond characterization

Analysis of the compliance and energy release rate of the sandwich double cantilever beam (DCB) specimen is presented. It is assumed that there is a starter crack at the upper face/core interface and that the crack remains at or near this interface during crack propagation. Beam, elastic foundation, and finite element analyses are presented and compared to experimentally measured compliance data, and compliance calibrated energy release rate over a range of crack lengths for foam cored sandwich DCB specimens. It is found that the beam analysis provides a conservative estimate on the compliance and energy release rate. The elastic foundation model is in agreement with finite element analysis and experimental compliance data. Recommendations for specimen design and an expression for an upper limiting crack length are provided.     

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90° unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.     

An analysis of the crack tip fields in a ductile three-point bend specimen subjected to impact loading

Analyses of an impact fracture test of a precracked, three-point beam of HY100 steel were performed to determine the dynamic fracture toughness. During impact, the crack tip opening displacement (CTOD) 100 μm behind the crack tip was measured using an optical measuring device called the interferometric strain/displacement gage. Since fracture initiates when stress wave effects dominate, a numerical simulation of the fracture event was conducted to obtain relevant near crack tip field parameters. The specimen was modeled by a plane stress finite element simulation using a rate sensitive elastoplastic material law. Since the simulated CTOD was to be compared with the measured CTOD in a region of residual strains due to crack closure, this effect was included in the model. The simulation produces a CTOD versus time response within 10% of the observed response, indicating that the other field quantities (such as the J-integral) should also be reliable. The loading rate /.K₁ was approximately 8 × 10⁶MPa√m/sec. If the fracture initiation time is assumed to coincide with the time at which the simulated and observed CTOD curves diverge, then the impact fracture toughness is 56% higher than the static fracture toughness.     

Supersmall punch test to estimate fracture toughness JIc and its application to radiation embrittlement of 2.25Cr-1Mo steel

A supersmall punch test has been used to extract fracture strain information on irradiated 2.25Cr-1Mo steel from transmission electron microscopy disc specimens as small as 3 mm in diameter and 0.25 mm in thickness. The test is based on driving a steel ball punch through a clamped specimen. The size effect of biaxial equivalent fracture strain of various kinds of materials and irradiated steel has been demonstrated. The results of fracture strain obtained from specimens 3 mm in diameter has been related almost linearly to the fracture toughness J_Ic for elastic and plastic behaviour. The relationship between fracture strain and fracture toughness J_Ic has been verified for the irradiated nuclear pressure vessel steel 2.25Cr-1Mo so that large amounts of irradiation space in nuclear reactor could be saved.     

On the use of constraint parameter A2 determined from displacement in predicting fracture event

The constraint based fracture mechanics methodology, J–A₂ method, has been used to interpret cleavage fracture recently. In all previous studies, the constraint parameter A₂ was determined by stresses analytically calculated from finite element analyses (FEA). In the current paper, it is first demonstrated that A₂ can be measured during a fracture test using the crack tip opening displacement (CTOD). A single-edge-notched specimen under bending (SENB) is used to compare the A₂ values determined from δ₅ displacement and the stress components. Finally, cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at −40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and the University of Kansas (KU) are interpreted using the J–A₂ analytical model. Particular emphasis is placed on using the A₂ determined from CTOD to characterize the fracture event. It is demonstrated that the effects of crack depth (shallow vs deep) and specimen size (small vs large) on the fracture toughness from the test programs can be interpreted and predicted using J and the constraint level A₂ measured from the displacement.     

A simplified beam analysis of the end notched flexure mode II delamination specimen

A modified classical beam theory solution is developed for the end notched flexure (ENF) specimen, one of the most widely used mode II delamination tests for fibre reinforced composite materials. The effect of crack tip deformation is analyzed by assuming that a region of certain length close to the crack tip rests on an elastic shear spring foundation. The mathematical procedure of the present analysis is simple and clear, and the resulting solutions for the compliance and the strain energy release rate of the ENF specimen are highly accurate. Excellent agreement is obtained over a wide range of material and geometrical properties of ENF specimens when the current results are compared with finite element results and other analytical analyses that include the effect of crack tip deformation in their solutions. The success of the present analysis indicates that the effect of crack tip deformation is the most important factor that must be considered when calculating the relationship between G_II and the load in the ENF specimen.     

New ‘ηpl'' and ‘γ'' functions to evaluate J–R curve from cracked pipes and elbows. Part II: experimental and numerical validation

Experimental evaluation of J–R curve in a crack growth situation requires ‘η_pl' and ‘γ' functions that are specific to a cracked geometry and loading condition. In Part I [Engng. Fract. Mech., in press] of this paper, new η_pl and γ functions, which are not available in the literature, for pipe and elbow geometry with various crack configurations under different loading conditions have been derived. In this paper, some of these newly proposed η_pl and γ functions have been validated experimentally through comparison of crack initiation load and J–R curve. In few cases, numerical validation has also been provided by comparing the J-integral values calculated through η factor approach and finite element method.     

Characteristics of brittle fracture under general combined modes including those under bi-axial tensile loads

In this paper, the brittle fracture initiation characteristics under general combination of the opening mode (Mode I), sliding mode (Mode II) and tearing mode (Mode III) were investigated both theoretically and experimentally.

First, the perfectly brittle fracture tests were conducted on specimens of PMMA (Polymethylmethacrylate) for all possible combinations of the fracture modes including respective pure modes. The experimental fracture strengths were compared with those predicted by the fracture criteria which are represented in terms of: (1) maximum tangential stress, [σ_gq]_max, extended to general combined modes, (2) maximum energy release rate at the propagation of a small kinked crack, [G^k(γ)]_max, and (3) newly derived maximum energy release rate at the initiation of a small kinked crack, [G(γ)]_max. It was found that the [G^k(γ)]_max or [G(γ)]_max criterion was very effective to predict both the direction of initial crack propagation and the fracture strength. These energy release rates are expressed in closed forms, and the interaction curves of the brittle fracture strength under arbitrary combinations of Modes I, II and III were derived.

Next, for fracture accompanied by plastic deformation, tests were carried out on specimens of mild steel (SM 41) imposing bi-axial tensile loads at various low temperatures. Then, brittle fracture with plastic deformation occurs under a combination of Modes I and II. In the case of brittle fracture with small scale yielding, the [G(γ)]_max criterion predicts well the direction of initial crack propagation but estimates only lower fracture strength than the experimental one. In the cases of brittle fracture with large scale yielding and under general yielding, it was found from the fracture tests that the direction of initial crack propagation was nearly normal to the resultant vector of the crack opening displacements in the opening and sliding modes at the notch tip. To this type of fracture, the modified COD criterion predicts well the direction of initial crack propagation, but lower fracture strength.

When brittle fracture occurs under the influence of plastic deformation, in such cases as the last three mentioned above, the actual fracture strength is higher than what the most reliable criterion predicts and it increases as deformation in Mode II becomes larger.     

The One-Point Method as Clinical Tool to Calculate and/or Adjust Dosage Regimen

The one-point method is presented as clinical tool to calculate the dosage regimen for patients where differences in steady state blood levels are expected due to change in volume of distribution (edema, obesity, myocardial or coronary infarction, hypoalbuminemia, displacement from protein binding, etc). The one-point method is based on the c_min'. - and superposition methods using a single blood sample upon administration of a test dose during the first dosing interval.

This method is indicated when assessment of the dosage regimen is complicated by a change in either the volume of distribution, V_d, or the elimination rate constant, k,_el or when the distribution coefficient. δ, is not known. There are various clinical situations in which V_d, is altered, such as in patients with edema, obesity, recent coronary or myocardial infarction, hepatic failure, hypoalbuminemia, displacement from protein binding due to other concomitantly given drugs, etc.     

Weight function calculations for mixedmode fracture problems with the virtual crack extension technique

An efficient finite element method is presented for calculating the stress intensity factors (K_I and K_II) and the weight functions for mixed-mode cracks with one virtual crack extension. The computational efficiency is enhanced through the use of singular elements and the application of colinear virtual crack extension (VCE) technique to symmetric mesh in cracktip neighborhood. This symmetric mesh in crack-tip vicinity permits the analytical separation of strain energy release rate into G_I for Mode I and G_II for Mode II for the mixed fracture problems with the colinear virtual crack extension.

Rice's displacement derivative representation of weight function vector for symmetric crack has been extended to the mixed fracture mode at nodal location (x_i,y_i) with crack length (a) and inclination angle (β) as h_I(II)(x_i, y_i, a, β) = (H/2K_I(II)(∂U_I(II)(x_i, y_i, a, β/∂a).

This equation permits explicit determination of weight functions for the entire structure of a given asymmetric crack geometry with colinear VCE technique. The explicit weight functions for mixed fracture mode depend strongly on the constraint conditions. The method of obtaining the required stress intensity factors of a given asymmetric crack geometry, from the weight function concept under the selected constraint conditions, which are different from constraint conditions used in the available weight functions for the same crack geometry, is also presented in this paper. This is accomplished by combining the predetermined explicit weight functions with the self-equilibrium forces at their application locations. These self-equilibrium forces include both the applied surface tractions and the reaction forces induced from the constraint conditions.