Non-propagating cracks and high-cycle fatigue failures in sharply notched specimens under in-phase Mode I and II loading

Sharply notched specimens were tested under in-phase Mode I and II loading to study the non-propagating crack behaviour in the presence of complex stress states. The material employed in the present investigation was a commercial low carbon steel. Non-propagating cracks were generated under different ratios between Mode I and Mode II stress components. The direct inspection of the cracked samples showed that the early stage of the crack propagation was mixed Mode governed (Stage 1-like process), whereas the subsequent propagation was seen to be mainly Mode I dominated (Stage 2-like process). Moreover, it was observed that non-propagating crack length tended to increase as the Mode II contribution to fatigue damage increased. In any case, independently of the degree of multiaxiality, their average length was of the order of 2L, where L was the material characteristic length calculated according to the theory of critical distances. Finally, the detected crack paths were used to form some hypotheses on the reason why two methods previously formulated by the authors are successful in predicting the multiaxial high-cycle fatigue strength, even though they make quite different assumptions on the physical mechanisms damaging metallic materials in the high-cycle fatigue regime.     

FATIGUE CRACK GROWTH UNDER MODE II LOADING

Abstract— The behavior of fatigue crack growth for low and medium carbon steels, an austenitic stainless steel and an aluminum alloy under pure Mode II loading was investigated experimentally, using cruciform specimens. The results show that under pure Mode II loading, fatigue crack propagation has three possibilities, namely, bifurcation into two branches, propagation along the original Mode II direction, and the mixture of these two situations, depending on the material. The growth rate da/dN vs. ΔK_II relation for Mode II propagation is similar to a Pans type law for Mode I growth. Fractographic observations by optical microscopy and SEM were made also on all specimens tested. When a crack branched, striations parallel to the crack front which were often associated with Mode I fatigue crack growth were observed and long marks parallel to the crack propagation direction were also found for slanted fracture surfaces. When a crack propagated along the original Mode II direction, many frictional marks parallel to the crack propagation direction were observed.     

Analysis of mixed-mode cracks in a rubbery particulate composite

The mixed-mode loading of a rubbery particulate composite is studied experimentally. Linear fracture mechanics concepts are used to determine the initiation of growth, the initial growth direction, and the subsequent growth rate for a range of mode mixities. The fracture toughness locus is determined to be elliptical, with the Mode II toughness being lower than its Mode I counterpart. The initial growth directions correlate with maximum strain energy density theories. The crack growth rates can be modeled effectively using an equivalent Mode I crack.     

Mixed mode stable tearing of thin sheet?AI 6061-T6 specimens: experimental measurements and finite element simulations using a modified Mohr-Coulomb fracture criterion

In this investigation, a combined experimental and computational approach with a Modified Mohr Coulomb (MMC) fracture criterion employing post-initiation element softening is used to simulate stable crack propagation under Mode I, Mode III and combined Mode I/III loading conditions. Results from the studies demonstrate that good correlation exists between the measured load-displacement and the numerically predicted response when the stiffness of the specimen fixture is included in the FE model. The numerical results were able to capture most of the experimentally observed features during crack propagation, such as through-thickness slant fracture, necking, tunneling and local specimen twist, thus confirming that the MMC criterion is suitable for predicting in-plane and out-of-plane tearing of sheets. It was found that in order to predict correctly the load-displacement curve as well as the fracture plane, different amount of softening is needed for Mode I and Mode III loading cases. This observation can be justified on the micro-mechanical level, while there is a competition between the mechanisms of dimple and shear fracture.     

Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes

Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and “S” shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens.     

Griffith's criterion for mixed mode crack propagation

The fracture criterion of mixed mode crack has been investigated extensively by many people on the basis of Griffith's theory. In this paper, the energy release rate of crack propagation along an arbitrary direction is obtained by the use of Griffith's theory. Then the general expression of the energy release rate criterion has been derived. The results have been compared with the measured data of the fracture testing under combined Mode II–III and Mode I–II–III loading.     

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.     

Mixed Mode I/II fatigue crack growth in adhesive joints

Fatigue crack growth (FCG) tests have been carried out on adhesively bonded compact tension-shear (CTS) specimens to assess the behaviour of a structural adhesive under Mixed Mode I/II conditions. The fractographic analysis revealed that energy dissipation mechanisms due to inelastic phenomena like bulk plastic deformation and crazing are more pronounced in Mode I than in Mixed Mode and Mode II. This is reflected by a FCG rate that increases going from Mode I to Mode II for a given value of the range of strain energy release rate, ΔG.     

A phenomenological analysis of Mode I fracture of adhesively-bonded pultruded GFRP joints

The fracture behavior of adhesively-bonded pultruded joints was experimentally investigated under Mode I loading using double cantilever beam specimens. The pultruded adherends comprised two mat layers on each side with a roving layer in the middle. An epoxy adhesive was used to form the double cantilever beam specimen. The pre-crack was introduced in three different depths in the adherend in order to induce crack initiation and propagation between different layers and thus investigate the effect of these different crack paths on the strain energy release rate. Short-fiber and roving bridging increased the fracture resistance during crack propagation. Specific levels of critical strain energy release rates could be attributed to each of the crack paths, with their levels depending on the amount of short-fiber bridging and the presence of a roving bridge. The different levels of critical strain energy release rate could be correlated to the morphology of the fracture surface and the strain energy release rate can thus be determined visually without any measurement.     

Experimental studies on mixed‐mode dynamic fracture behaviour of aluminium alloy plates with narrow U‐notch

Mixed‐mode dynamic fracture behaviour of cast aluminium alloy ZL205A thin plates with narrow U‐notch was studied by split Hopkinson tensile bar apparatus. Specimens with different loading angles were designed to realize different fracture modes. The same loading condition was maintained during the tests. Recovery specimens show that crack propagates along the notch direction. Force–elongation relations show that with the loading angle increasing, the fracture force increases while the final elongation decreases. Deformation and fracture process was observed by a high‐speed camera. Displacement distribution around the crack was calculated through digital image correlation technique. Based on the photos and displacement results, initiation time of the crack was derived. Besides, two stress components (normal stress and shear stress) applied on the fracture surface were investigated. Results show that crack initiation stresses at different loading angles satisfy the ellipse equation. Pure mode I and II fracture stresses are 425.3 and 236.7 MPa, respectively. Furthermore, specific fracture energy of different specimens was calculated. The energy data vary with loading angle and located on an approximate upward parabolic curve. From the curve, the minimum specific fracture energy of the thin plate specimen is 42.0 kJ/m² under loading angle of 76.3°.     

Connecting the essential work of fracture, stress intensity factor, Hill’s criterion in mixed mode I/II loading

Ductile sheet structures are frequently subjected to mixed mode loading, resulting that the structure is under the influence of a mixed mode stress field. Instances of interest are when stable crack growth occurs and when the crack-tip is propagating in this complex mixed-mode condition, prior to final fracture. Purposely designed apparatus was built to test thin-sheets of steel (Grade: DX51D) under mixed-mode I/II. These tests, under plane stress conditions, also investigated the effect of thickness on the specific essential work of fracture or the fracture toughness of the material under quasi-static cracking conditions. The fracture toughness is evaluated under incremental mixed-mode loading conditions. The direction of the propagating crack path and fracture type were observed and discussed as the loading mixity was varied. Whilst the specific essential work of fracture or fracture toughness was obtained using the energy approach, the theoretical analysis of the fracture type and direction of crack path were based on the crack tip stresses and fracture criterions of maximum hoop stress and maximum shear stress along with the utilisation of Hill’s theory. For mixed-mode I/II loading, the variation in the fracture toughness contributions ratios are evaluated and used predicatively using the established energy criterion approach to the crack tip stress intensity approach. The comparison between the theoretical directions of the crack path, failure mode propagation are in good agreement with those obtained from experimental testing indicating the definite link between both approaches.     

Influence of the matrix constituent on mode I and mode II delamination toughness in fiber-reinforced polymer composites under cyclic fatigue

Mode I and mode II fracture behaviour under static and dynamic loading was analyzed in two composites made up of the same reinforcement though embedded in two different matrices. Specifically, the delamination energy under static and dynamic loading was obtained for both materials and both fracture modes, i.e. the number of cycles necessary for the onset of fatigue delamination. Subsequently, the crack growth rate (delamination rate) was obtained for different percentages of the critical energy rate. The main goal of the study was to ascertain the influence of the matrix on the behaviour of the laminate under fatigue loading.From the experimental results for the onset of delamination, similar fatigue behaviour was observed at a low number of cycles for both matrices and both fracture modes, while in fatigue at a high number of cycles, a higher fatigue limit was obtained in the composite with the modified resin (higher toughness) for both fracture modes. From the point of view of crack growth rate, both materials behaved similarly for different levels of stress under fatigue and the two fracture modes for small crack lengths (initial growth zone < 5 mm), although the growth rate increased for large crack lengths. This behaviour was the same in both loading modes.     

Softening and snap-back instability in cohesive solids

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (K_I = K_IC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.     

Mixed mode fracture toughness of GFRP composites

Glass fibre reinforced polymer (GFRP) composites are used in a wide range of applications as a structural material. They have high specific mechanical properties but are prone to delamination as a result of manufacturing defects and impact/shock loading. The ability of the structure to continue to carry load after damage and the subsequent propensity of the damage to propagate are important considerations for the design of damage tolerant composite structures. In order to accurately predict the stability of damage under load, relevant mechanical properties of the material must be accurately determined. In particular, mixed mode fracture toughness data is required in order to study the damage criticality in such structures. This paper describes an experimental study to determine Mixed Mode fracture toughness for thick glass/vinylester specimens. The test methodology used for the experiments and its difficulties will be discussed. Mixed mode fracture toughness results are presented, as are Mode I and Mode II fracture toughness results obtained via Double Cantilever Beam (DCB) and End Notch Flexure (ENF) tests, respectively.     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

Sickle-shaped crack in a round bar under complex Mode I loading

A sickle‐shaped surface crack in a round bar under complex Mode I loading is considered. First, the stress‐intensity factor (SIF) along the front of the flaw is numerically determined for five elementary Mode I stress distributions (constant, linear, quadratic, cubic and quartic) directly applied on the crack faces. The finite element method and linear elastic fracture mechanics concepts are employed. Then, a numerical procedure to calculate approximate values of SIF for a complex Mode I stress distribution on the crack faces is proposed based on both the power series expansion of the function describing such a stress distribution and the superposition principle. In order to validate the results obtained through the above procedure, a comparison with numerical data available in the literature is made.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.     

Experimental study of I + III mixed mode fatigue crack transformation propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the mode transformation process. It is found that with the crack growth, I + III mixed mode changes to Mode I. Crack mode transformation is governed by the Mode III component and the transformation rate is a function of the relative magnitude of the Mode III stress intensity factor. However, even in the process of the crack mode transformation the fatigue crack propagation is controlled by the Mode I deformation.     

Experimental and numerical studies on dynamic crack growth in layered slate rock under wedge impact loads: part I—plane strain problem

The experimental and numerical investigations presented in this paper were carried out to determine the splitting forces and crack propagation scenarios of naturally bedded layered slate rock. Splitting loads were determined by impact splitting of regular‐sized slate blocks under plane strain test loading conditions, using a hydraulic actuator with a wedge‐shaped indenter. The mechanical properties of slate blocks required for numerical analyses were obtained from detailed experimental testing. The velocity of dynamic crack propagation in slate blocks under indenting wedge impact loading was determined using a series of strain gauge sensors. Numerical studies were carried out using ABAQUS, a general purpose, finite element analysis (FEA) program. Mode I dynamic crack propagation was simulated numerically by the gradual releasing of the restrained node on the symmetric plane of the specimens. Mode I stress intensity factors were computed for different crack lengths and the results were compared with the plane strain material fracture toughness obtained from earlier experiments/FEA. Very good agreement was obtained between analysis results and the measured fracture toughness value of slate, for the applied impact splitting load. Using the equation derived from a parametric study, of results obtained from the numerical analysis of different sizes of slate blocks, the maximum theoretical impact splitting force was determined using the plane strain fracture toughness value obtained from FEA. The difference between the loads obtained from the experimental studies and the derived empirical equation, varied between + 4.96% and −32.34%.     

CORROSION FATIGUE FRACTURE BEHAVIOUR OF A SiC WHISKERALUMINIUM MATRIX COMPOSITE UNDER COMBINED TENSIONTORSION LOADING

We describe an investigation into the fatigue fracture behaviour under combined tension–torsion loading of a SiC whisker-reinforced A6061 aluminium alloy fabricated by a squeeze casting process. Special attention was paid to the environmental effects on fatigue fracture behaviour. Tests were conducted on both the composite and its unreinforced matrix material, A6061-T6, under load-controlled conditions with a constant value of the combined stress ratio, α = τ_max /σ_max in laboratory air or in a 3.5% NaCl solution at the free corrosion potential. The corrosion fatigue strength of both the matrix and composite was less in the solution than in air. The dominating mechanical factor that determined the fatigue strength in air was either the maximum principal stress or the von Mises-type equivalent stress, depending on the combined stress ratio. However, in the 3.5% NaCl solution, the corrosion fatigue strength of both materials was determined by the maximum principal stress, irrespective of the combined stress ratio. In the case of the matrix material, crack initiation occurred by a brittle facet normal to the principal stress due to hydrogen embrittlement. However, in the composite material, the crack was initiated not at the brittle facet, but at a corrosion pit formed on the specimen surface. At the bottom of the pit, a crack normal to the principal stress was nucleated and propagated, resulting in final failure. Pitting corrosion was nucleated at an early stage of fatigue life, i.e. about 1% of total fatigue life. However, crack initiation at the bottom of a pit was close to the terminal stage, i.e. about 70% or more of total fatigue life. The dominating factor which determined crack initiation at a pit was the Mode I stress intensity factor obtained by assuming the pit to be a sharp crack. Initiation and propagation due to pitting corrosion and crack growth were closely examined, and the fatigue fracture mechanisms and influence of the 3.5% NaCl solution on fatigue strength of the composite and matrix under combined tension–torsion loading were examined in detail.