Hybrid specimens eliminating stress concentrations in tensile and compressive testing of unidirectional composites

Two novel approaches are proposed for elimination of stress concentrations in tensile and compressive testing of unidirectional carbon/epoxy composites. An interlayer hybrid specimen type is proposed for tensile testing. The presented finite element study indicated that the outer continuous glass/epoxy plies suppress the stress concentrations at the grips and protect the central carbon/epoxy plies from premature failure, eliminating the need for end-tabs. The test results confirmed the benefits of the hybrid specimens by generating consistent gauge-section failures in tension. The developed hybrid four point bending specimen type and strain evaluation method were verified and applied successfully to determine the compressive failure strain of three different grade carbon/epoxy composite prepregs. Stable failure and fragmentation of the high and ultra-high modulus unidirectional carbon/epoxy plies were reported. The high strength carbon/epoxy plies exhibited catastrophic failure at a significantly higher compressive strain than normally observed.     

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the −45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.     

Size effect of concrete members applied with flexural compressive stresses

In this study, two types of special experiments are carried out to understand flexural compressive strength size effect of concrete members. The first type is an ordinary cylindrical specimen (CS) with a fully penetrated and vertically standing plate type notch at the mid-height of the specimen, which is loaded in compression at the top surface (e.g., in the parallel direction to the notch length). The second type is a general double cantilever beam (DCB), which is compression loaded in axial direction (e.g., in the parallel direction of the notch). For CS, an adequate notch length is taken from the experimental results obtained from the compressive strength experiment of various initial notch lengths. The trial tests to select the effective initial notch length show that CS with an initial notch length approximately greater than four times the maximum aggregate size fails without an additional increased load and in stable manner under Mode I failure mechanism. Therefore, the initial notch length to the maximum aggregate size ratio of 4.0 is used for all size specimens. For DCB, the eccentricity of loading points with respect to the axial axis of each cantilever and the initial notch length are varied. In both specimens, the compressive loads apply flexural compressive stresses on the crack tip region of the specimens. These two types of specimens fail by Mode I crack opening mechanism. By testing 3 geometrically proportional size specimens for CS and DCB, the experimental datum for flexural compression size effect of concrete are obtained. Using the obtained flexural compressive strength size effect datum, regression analyses are performed using Levenberg-Marquardt's least square method (LSM) to suggest new parameters for the modified size effect law (MSEL). The analysis results show that size effect is apparent for flexural compressive strength of specimens with an initial notch. For CS, the effect of initial notch length on flexural compressive strength size effect is apparent. For DCB, flexural compressive size effect is dependent on the eccentricity of loading points with respect to the axial axis of the cantilever beam. In other words, if DCB specimen is applied with greater tensile stress at the crack tip, the size effect of concrete becomes more distinct. The results show that the flexural compressive strength size effect of initial notch length variation of DCB exists but directly dependent on the loading location. This is due to the fact that the sizes of fracture process zone (FPZ) of all DCB specimens are similar regardless of the differences in the specimen slenderness ratio, but the flexural compressive and tensile stress combinations resulting in stress concentration at the crack tip region has direct effect on size effect of concrete members.     

A new method for evaluating fracture toughness of brittle materials

A new testing procedure is suggested for measuring the fracture toughness of brittle materials as superconductors and ceramics. The idea is to perform a compression test on a subcompact square specimen which contains a central hole. The presence of the hole induces a tensile stress at a certain small region attached to the hole. In this region an artificial notch is introduced such that the fracture path satisfies a pure tensile opening mode (mode I) to which the linear fracture mechanics rules apply. The stress distribution on the fracture plane guarantees a certain amount of stable crack extension. The relationship between the critical compressive load and the stress intensity factor is formulated via an available Green function along with a numerical solution (FEM with ANSYS code). The testing procedure is demonstrated with specimens made of two types of tungsten carbide which differ by their grain size only. Test results are examined via fracture toughness and strength values produced by other conventional methods and the agreement is very good. The geometry and loading direction enable the fracture toughness results to be relatively insensitive to the notch tip radius and the crack length, thereby relaxing the requirements for accurate measurements.The small size of the suggested specimen (12.70mm×12.70mm×5mm) and the avoidance of gripping interfaces provide the major cost-wise advantages.     

Fracture of quasi-isotropic composite sheets with sharp notches

Continuous fibre composites are materials that exhibit rather linear elastic deformation behaviour: suggesting brittleness and notch sensitivity. However, notched composites may sustain significant mechanical load. The notch resistance of composites is investigated on quasi-isotropic composite sheets with sharp crack like notches. This allows the use of analytic solutions of the stress field around a crack in a similar way as is used for linear elastic fracture mechanics (LEFM) in homogeneous isotropic solids. Similar to the small scale yielding boundary condition in fracture mechanics, applied on homogeneous isotropic solids, a small-scale non-linear damage condition should be fulfilled for valid LEFM application on quasi-isotropic composites. Indeed, it appeared to be possible to define critical stress intensity factors (K_1c) for the quasi-isotropic composite. Moreover, K_1c values can quantitatively be related to laminate parameters and to the related damage and deformation processes occurring in a small near crack tip zone with intense non-linearity and strain gradients in the thickness direction. Before the final explosive fracture occurred, stable crack growth was observed. This could be described with R-curves, as done for homogeneous metal sheet specimens. Indeed, also in this case, the R-curves were identical, independent of the length of the initial crack-like notch. The R-curves can be estimated adopting a crack-bridging model. Crack growth occurs at the notch tip in the 0° plies. The other plies bridge the fractured 0° plies. The fracture mechanisms, determining the K_1c-values and the shape of the R-curve, are quite different for composites and metals. Yet, the method of fracture mechanics, well established for metals, can obviously also be applied to quasi-isotropic composites.     

Characterizing Mode II Delamination Cracks in Stitched Composites

This paper deals with characterizing the bridging mechanisms developed across delamination cracks by through-thickness reinforcement, using stitched carbon/epoxy laminates under mode II loading as a prime example. End Notched Flexure (ENF) tests are performed which show that stitching can provide stable crack growth. The bridging law, which characterizes the bridging action of the stitches, is deduced from both crack profile measurements and load vs. deflection curves. Consistent results are obtained from the two methods. The inferred laws imply that delamination cracks will commonly grow in conditions that are neither accurately nor properly described by linear elastic fracture mechanics. Large scale bridging calculations are required, in which the essential material property is the bridging traction law. The level of detail in which the law must be determined can be inferred from the sensitivity of predicted crack growth to variations in the law. It is recommended that the required parametric traction law be deduced in engineering practice from load vs. deflection data from the standard ENF (or similar) test, with due regard to selecting the notch size and other specimen dimensions to ensure that crack growth is stable in the test. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fatigue damage mechanics of composite materials Part III: Prediction of post-fatigue strength

A damage-based model for post-fatigue notch strength is presented. The model is an extension of a method developed previously to predict the notch strength of laminated composites. A simple finite element representation of the notch tip damage zone is used to obtain the localized damage-modified stress distribution. A uniaxial tensile stress failure criterion is applied to the 0° plies from which the laminate strength is evaluated. In conjunction with the fatigue damage growth law described in Part II, residual strength is calculated as a function of the applied loading conditions, specimen geometry and lay-up for (90/0)_s, (90/0)_2s and (90₂/0₂)_s T300/914C carbon-fibre/epoxy laminates subjected to tension-tension fatigue cycling.     

A method for evaluating the thermal fatigue resistance of ceramics and its application to a fibre reinforced refractory material

An original method of characterizing thermal fatigue of ceramic materials has been proposed. This method is based on after-shock measurements of the degree of damage through a compliance calibration using compact tension (CT) test pieces. This method has been applied to a fibre-reinforced refractory material subjected to repeated thermal shock between 20 and 800° C. It has been demonstrated from both experiments and finite element analysis that the CT specimen is a convenient shape for the evaluation of thermal fatigue behaviour. In these specimens it has been established that the damage primarily affects the notch tip. The thermal fatigue behaviour of the CT specimens depends on notch length: when the notch length is greater than 30 mm, catastrophic failure occurs after a few cycles. When the notch length is less than 30 mm, the crack formed at the notch tip during the first cycle grows slowly during subsequent cycles. This behaviour has been explained by the variation of the stress intensity factor K _I.     

Notch sensitivity of fiber-reinforced ceramics

Crack bridging from an elliptical hole in fiber-reinforced ceramic composites is studied. For some fiber-reinforced ceramic composites, matrix toughness is much less than the toughness gained in the bridging zone, i.e. the bridging zone runs across the entire width of a specimen at a small load. In such case, load-carrying capacity of the specimen only depends on one parameter which is the measure of notch sensitivity. Solving the crack bridging problem for various aspect ratios of the elliptical hole and various bridging law shapes, the role of crack bridging from the hole is determined. The results presented may be used to guide design in addition to providing an improved understanding of the mechanism of fiber-matrix failure.     

A numerical study of the elastic stress field arising from sharp and blunt V-notches in a SENT-specimen

The elastic stress field arising from a V-notch in a Single Edge Notched Tension (SENT) specimen is studied using the Sherman–Lauricella integral equation. Accurate values of the generalized stress intensity factor, here denoted Q _I, are determined and compared with values from the literature. A Q _I-dominated distance ahead of the notch tip is defined and determined for several notch angles and different notch depth to specimen width ratios. It is found that for depth to width ratios over 0.45 the Q _I-dominated distance is approximately constant while below this value the distance can show a great variation with the notch angle. Additionally, a general formula for the maximum stress in a V-notch with a finite root radius is derived. Its applicability on the SENT-specimen is studied and presented as a family of curves. If used within these curves, the formula can accurately predict stress concentrations, even for very smooth notches.     

R-curve behavior in fracture of notched porous ceramics

Notched specimens of porous silicon carbide (SiC) with porosity 37% were fractured under four-point bending. A single edge notch with six depths ranging from 0.1 to 2.8 mm was introduced to the specimen with a height of 7 mm. The fracture of specimens with a notch depth of 0.1 mm did not start from the notch, but from the intrinsic defect. The size of the non-damaging notch is about 0.1-0.2 mm and roughly equal to the size of SiC particles. When the notch depth was larger than 0.4 mm, the fracture started from the notch for all specimens. The record of the strain gage glued on the compression surface of the specimen as a function of the load showed nonlinearity before reaching the maximum load. The critical stress intensity factor was nearly constant for crack initiation from the notch. The resistance curve was constructed by estimating the crack length from the compliance change of the specimen, and was used for determining the maximum load point in bending tests. Fractographic observations showed the fracture path along the binder phase between silicon particles.     

Fracture mechanics solutions to spot welds

Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.     

Fatigue of shot peened 7075-T7351 SENB specimen – A 3-D analysis

As‐received or shot peened 7075‐T7351 single‐edged notch bend (SENB) specimens, 8.1‐mm thick, were fatigued at a constant maximum load and at stress ratios of R= 0.1 and 0.8 to predetermined numbers of fatigue cycles or to failure. The SENB specimens were then fractured by overload and the tunnelling crack profiles were recorded. The crack‐growth rate, da/dN, after crack initiation at the notch was determined by crack‐profile measurement and fractography at various fatigue cycles. The shot peened surface topography and roughness was also evaluated by three‐dimensional (3‐D) laser scanning microscopy. Residual stresses in the as‐received specimens and those generated by shot peening at Almen scales of 0.004A, 0.008A, 0.012A and 0.016A, were measured by an X‐ray diffraction stress analyser with an X‐ray target, CrK, every 0.1 mm to a depth of 1 mm. The 3‐D stress intensity factor of the curved crack front was determined by the superposition of the 3‐D finite element solutions of the stress intensity factor of the loaded SENB specimen without the residual stress and the stress intensity factor of the unloaded SENB specimen with a prescribed residual stress distribution. da/dN versus the resultant stress intensity factor amplitude, ΔK_I, plots showed that while the residual stress locally retarded the crack‐growth rate it had no effect on the overall crack‐propagation rate.     

On the fracture of small samples under higher order strain gradient plasticity

In this work we perform Finite Element simulations within the framework of large deformation elasto-viscoplasticity on a material that is sensitive to the gradients of plastic strain and incorporates a single intrinsic length scale parameter. Both small scale yielding simulations and those on a finite sized sample show that large stress enhancements can occur at the tip of a notch due to gradient effects. The amount of plastic strain and opening stress that can be expected at the notch tip depends on an interplay between the notch radius, specimen dimensions and boundary conditions. It is shown that cleavage can be the favored criterion for failure in even a ductile material when the notch radius is small compared to the intrinsic length scale. Moreover, for large intrinsic length scales, failure may not always initiate at a notch but may be triggered away from it due to the presence of a boundary impermeable to dislocations.     

Effect of loadline shift on applied crack tip stress intensity in WOL specimens

A change in applied stress intensity due to shifting of load line from the pin hole to a wedge located on the outside edge of the notch has been investigated by: (1) finite element analysis, (2) measurements of front face crack opening displacement and (3) strain relaxation near the crack tip.

Results show that this wedge loading procedure will result in a significant drop, up to a factor of two, in applied stress intensity. The drop in stress intensity is inversely related to the crack length (expressed by a/W). This drop in stress intensity is due to overall specimen distortion because of load line shift and local deformation of the wedge and notch surfaces. Implications of this drop on Stress Corrosion Cracking results are discussed. For reliable stress corrosion testing, modifications in specimen geometries and loading procedures are suggested.     

Fracture behaviour of a TiAl alloy under various loading modes

Tensile tests, compression tests, in situ tensile tests, bending tests, tensile fatigue tests and bending fatigue tests were carried out for a TiAl alloy. Based on the global experimental results and microscopic observations of the fracture surfaces and cracking behaviour on the side surfaces of tested specimens, the fracture mechanisms of fully lamellar (FL) TiAl alloys under various loading modes are summarized as following: (1) Cracks initiate at grain boundaries and/or interfaces between lamellae. (2) When a crack extends to a critical length, which matches the fracture loading stress the crack propagates catastrophically through entire specimen. (3) The crack with the critical length can be produced promptly by the applied load in the tensile and bending test or be produced step-by-step by a much lower load in the fatigue tensile test. (4) For fatigue bending tests, the fatigue crack initiates and extends directly from the notch root, then extends step-by-step with increasing the fatigue bending loads. The fatigue crack maybe extends through entire specimen at a lower fatigue load or triggers the cleavage through the whole specimen at a higher load. (5) In compressive tests, cracks initiate and propagate in directions parallel or inclined to the compressive load after producing appreciable plastic strains. The specimen can be fractured by the propagation of cracks in both directions.     

Crack propagation from a pre-existing flaw at a notch root. I. Introduction and general form of the stress intensity factors at the initial crack tip

This paper and its companion are devoted to the study of crack kinking from some small pre-existing crack originating from a notch root (the notch root radius being zero). Both the notch boundaries and the initial crack are allowed to be curved; also, the geometry of the body and the loading are totally arbitrary. The ingredients required are knowledge of the stress intensity factors at the initial crack tip and use of a suitable mixed mode propagation criterion. This paper is devoted to the first point, and more specifically to establishing the general (that is, not yet fully explicit) form of the formulae giving these stress intensity factors. The method used is based on changes of scale (homogeneity properties of the equations of elasticity) on the one hand, and on continuity of the displacement and stresses at a given, fixed point with respect to the crack length on the other hand. The formulae derived for the stress intensity factors at the tip of the small crack are of universal value: they apply to any situation, whatever the geometry of the body, the notch and the crack and whatever the loading, the stress intensity factors depending always only upon the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the notch root in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack.     

Quantitative evaluation of the adhesion of metallic coatings using cylindrical substrate

This paper introduces an effective interfacial fracture toughness test based on interface fracture mechanics theory. This testing method uses a circumferentially notched tensile (CNT) specimen, which is ideally suited for determining the interfacial fracture resistance of coatings. Unlike other interfacial fracture tests, this test is simple to prepare, requires minimum test setup and is easy to model. An interfacial pre-crack was generated between a nickel coating and mild steel cylindrical substrate to evaluate adhesion strength. In situ acoustic and SEM analyses were used to determine the crack initiation or the critical load of failure. The critical energy release rate, critical stress intensity factors and phase angle were determined using the J integral which was determined by applying the critical load to the finite element model. A detailed finite element analysis was carried out to study the effect of different interface pre-crack positions and mode mixity on energy release rate for different notch angles and elastic modulus ratios. The cracking resistance of the interface was characterised by the notch angle of CNT specimens. The analysis showed an increase in interfacial fracture toughness as phase angle increases and was significant when the phase angle was large. The combined results of computational and experimental analysis showed that any defect or stress concentration at the interface could significantly weaken the adhesion of coating.     

Finite element analysis of bi-material interface notch crack behaviour

The finite element method is extended to the analysis of the behaviour of an interface crack in bi-material specimen with a central hole. First, only the notch effect is considered, the field of stress and variation of the stress concentration factor as a function of the Young’s modulus ratio are determined. Secondly, the notch interface crack behaviour is investigated, the variations of the stress intensity factor versus the Young’s modulus ratio and crack length are shown as well as the distribution of stresses in the plate and along the interface.     

Fatigue crack growth with fiber failure in metal-matrix composites

Crack growth during the fatigue of fiber-reinforced metal-matrix composites can be predicted analytically by determining the reduction in the crack tip stress intensity range resulting from fiber bridging. Various canonical functions exist that relate the crack tip stress intensity range to bridged crack geometries and loading for both infinite and finite width specimens; however, comprehensive crack growth predictions incorporating fiber failure require knowledge of the maximum fiber stress in the bridged zone for all notch sizes and crack lengths. Previous modeling efforts have been extended to predict complete growth curves with fiber failure for specimens of finite width. Functions for maximum fiber stresses in the bridged zone are presented here for a center crack in tension and edge cracks in tension and bending. The rapid increase in crack growth when fibers fail emphasizes the importance of determining the loads and notch sizes that mark the beginning of fiber failure. Critical loads for given notch sizes and fiber strengths are easily determined for finite width specimens using the functions presented in this work.