Study of slant fracture in ductile materials

Slant fracture is widely observed during crack growth in thin sheet specimens made of ductile materials, providing a good case for investigating three-dimensional criteria for mixed-mode ductile fracture. To gain an understanding of slant fracture events and to provide insight for establishing a slant fracture criterion, stable tearing fracture experiments on combined tension-torsion (nominal mixed-mode I/III) specimens and nominal Mode I Arcan specimens made of Al 2024-T3 are analyzed using the finite element method under three-dimensional conditions. Two types of finite element models are considered for the study of slant fracture: (a) combined tension-torsion specimens containing stationary, flat and slant cracks subject to loads corresponding to the onset of crack growth, and (b) stable tearing crack growth with slanting in a nominal Mode I Arcan specimen. Analysis results reveal that there exists a strong correlation between certain features of the crack-front effective plastic strain field and the orientation of the slant fracture surface. In particular, it is observed that (a) at the onset of crack growth in the combined tension-torsion experiments, the angular position of the maximum effective plastic strain around the crack front serves as a good indicator for the slant fracture surface orientation during subsequent crack growth; and (b) during stable tearing crack growth in the Mode I Arcan specimen, which experiences a flat-to-slant fracture surface transition, the crack growth path on each section plane through the thickness of the specimen coincides with the angular position of the maximum effective plastic strain around the crack front.     

Approximate formulae for estimating the j-integral of a circumferentially cracked round bar under tension or torsion

The approximate formulae for estimating the J contour integral by the use of a single load-displacement curve were newly derived for the circumferentially cracked round bar subjected to tensile (Mode I) or torsional (Mode II) loading, by paying attention to the elastic-plastic deformation behavior which is characterized by full yielding (net section of specimen is in yield) or general yielding (gross section of specimen is in yield). As application examples, elastic-plastic fracture toughness tests were performed at room temperature on Ni-Cr-Mo-V forged steel. The ductile crack growth resistance curves under the Mode I or the Mode III loading were measured with the multi-specimen method, and the fracture behaviors of each mode were examined.     

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε _θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.     

R-curve behaviour of a structural steel

The ductile tearing behaviour-of BS4360 50D structural steel has been studied using two bending specimen geometries: square (W = B) cross section three point bend specimens with different initial fatigue crack length, ranging from a/W = 0.20 to about 0.75, and rectangular cross section (W = 2B) specimens with initial fatigue crack length a/W = 0.3.With the first set of specimens it was intended to investigate the possible dependence of the tearing behaviour on initial crack length. It was concluded that specimens with shorter values of initial crack length present higher resistance to ductile tearing. Two different methods of calculating the J-resistance curve, one based on the approximate equation J = 2A/(W?a)B and a more elaborate calculation procedure introduced by Garwood were used. The curves determined following the more accurate procedure were used to determine the value of the tearing modulus T, which is related to the occurrence of tearing instabilities in structures. It was found that T decreases slightly with increasing value of initial crack length.The tests using the wider specimen geometry were intended to examine the tearing behaviour over a larger amount of crack growth allowed by the wider geometry used. It was found that the resistance curves, using the COD concept, present a maximum after which the resistance begins to drop. This maximum value of the COD-resistance curve is higher than the conventional δ_max measured at max load. These tests were performed using the compliance technique of evaluating the crack length. Tests performed with 10% unloading presented slightly lower values of resistance than tests performed with complete unloading.It was found that the relationship J = mσ_flowδδ presents increasing values of m with crack growth. This is attributed to an increasing local yield stress, caused by the through thickness deformation.     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

Mode I fatigue crack growth reduction mechanisms after a single Mode II load cycle

A single Mode II load cycle, large enough to create residual displacements, decreases the subsequent Mode I crack growth rate. The distance for Mode I crack growth rate to fully recover, i.e., revert to the same da/dN as before Mode II load, is much longer than Mode II plastic zone size. The higher Mode II load, the larger is the reduction in growth rate and the longer the recovery distance. Higher Mode I R-ratio means smaller reduction in growth rate. Above a certain R-ratio, no reduction occurs at all. In the present study it is found that the reduction in growth rate is solely caused by crack closure due to tangential displacement of crack-surface irregularities that induce a surface mismatch between the upper and lower crack faces. The mechanism is called Mode II-induced crack closure. A model based on both analytical and experimental results is developed in order to estimate the degree of Mode II-induced crack closure after a Mode II load.     

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.     

The effect of steady torsion on fatigue crack growth in shafts

Most of catastrophic mechanical failures in power rotor shafts occur under cyclic bending combined with steady torsion: Mode I (ΔK_I) combined with Mode III (K_III). An analysis of the influence of steady torsion loading on fatigue crack growth rates in shafts is presented for short as well as long cracks. Long cracks growth tests have been carried out on cylindrical specimens in DIN Ck45k steel for two types of testing: rotary or alternating bending combined with steady torsion in order to simulate real conditions on power rotor shafts. The growth and shape evolution of semi-elliptical surface cracks, starting from the cylindrical specimen surface, has been measured for several loading conditions and both testing types. Short crack growth tests have been carried out on specimens of the same material DIN Ck45k, under alternating bending combined with steady torsion. The short crack growth rates obtained are compared with long crack growth rates. Results have shown a significant reduction of the crack growth rates when a steady torsion Mode III is superimposed to cyclic Mode I. A 3D Finite Element analysis has also shown that Stress Intensity Factor values at the corner crack surface depend on the steady torsion value and the direction of the applied torque.     

The re-characterisation of complex defects: Part II: cleavage

The re-characterisation of complex defects with re-entrant sectors has been addressed for cracks extending by fatigue, ductile tearing and cleavage. In Part I crack extension by fatigue and ductile tearing was discussed. In Part II cleavage data are presented for a family of complex defects with re-entrant sectors. Experimental tests on complex and re-characterised profiles are analysed using deterministic and probabilistic approaches. The work addresses the conservatism of re-characterisation procedures when applied to cleavage failure on the lower shelf and in the ductile–brittle transition.     

CHARACTERIZATION OF DUCTILE TEARING RESISTANCE BY ENERGY DISSIPATION RATE

The J integral, which is widely used in elastic-plastic fracture mechanics, is not the true driving force any more if the crack is propagating. This leads to some inconsistencies when ductile tearing resistance is characterized in terms of J, especially for large crack extensions. Instead, Turner has proposed the energy dissipation rate as a physically more meaningful quantity. His concept is discussed and more evidence is given that will provide a better understanding of ductile tearing. It is shown how this quantity can be determined by measuring the heat production ahead of a fast running crack, or calculated in a finite element analysis, or re-evaluated from J-R test records of bend and tensile specimens. The energy dissipation rate is decreasing with crack extension in gross plasticity and approaches a stationary state. From these relations, the shapes of the cumulative J-R curves can be derived for different specimen geometries.     

An engineering interpretation of pop-in arrest and tearing arrest in terms of static crack arrest, KIa

When fracture toughness specimens are tested under displacement controlled conditions, they are often observed to exhibit unstable cleavage fracture followed by arrest of the cleavage mode wherein a significant load remains on the specimen (pop-in arrest). This behavior carries over into the ductile tearing regime wherein tearing may occur rapidly identified by load reduction and then proceeds at a discernible less rate (tearing arrest). Both these behaviors represent an initiation condition followed by an arrest condition. In this paper it is demonstrated that from either of the arrest conditions an arrest value may be determined which, for available experimental data, is shown to be an engineering estimate for the static crack arrest toughness, K_Ia. A general lower bound property for the arrest value is postulated based on referenced information.A data analysis procedure is outlined and K_Ic and K_Ia estimates from sixty-eight 1/2, 1 and 2 in. thick compact specimens from two steels (A533 Grade B Class 1 and AISI 1018) tested between -40°F and 200°F are summarized. The crack arrest estimates are seen to compare favorably with K_Ia results obtained by other investigators using 2 in. thick specimens. Also it is demonstrated that when failure is by fully ductile tearing, the crack arrest toughness is at least equal to the estimate for K_Ia for the specimen.It is judged that an engineering procedure has been demonstrated for obtaining reasonable estimates of K_Ia throughout the transition region and onto the upper shelf. Based on referenced work, shelf values are most likely specimen size dependent.     

A convenient way to represent fatigue crack growth in structural adhesives

The present paper examines crack growth in a range of aerospace and automotive structural adhesive joints under cyclic‐fatigue loadings. It is shown that cyclic‐fatigue crack growth in such materials can be represented by a form of the Hartman–Schijve crack‐growth equation, which aims to give a unique and linear ‘master’ representation for the fatigue data points that have been experimentally obtained, as well as enabling the basic fatigue relationship to be readily computed. This relationship is shown to capture the experimental data representing the effects of test conditions, such as R‐ratio and test temperature. It also captures the typical scatter often seen in the fatigue crack‐growth tests, especially at low values of the fatigue crack‐growth rate. The methodology is also shown to be applicable to both Mode I (opening tensile), Mode II (in‐plane shear) and Mixed‐Mode I/II fatigue loadings. Indeed, it has been demonstrated that the fatigue behaviour of structural adhesives under both Mode I and Mode II loadings may be described by one unique ‘master’ linear relationship via the Hartman–Schijve approach.     

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.     

Mixed mode fatigue crack propagation in a ferritic–perlitic cold drawn tube

Previous work by the authors has shown that torsional fatigue tests on cold drawn tube specimens with a longitudinal micronotch present both Mode III ahead of the crack tip (throughout the tube thickness) and Mode I at the defect edges. The co-planar Mode III propagation was prevalent and is followed by Mode II crack propagation along the cold drawn direction.In this work, this behaviour is further investigated by a new series of experimental tests together with a finite element analysis. The mechanisms behind this competition between Mode I and Mode III cracks are analysed and some fractographies were performed on run-outs, broken and interrupted tests.Indeed, pure Mode I and pure Mode II crack propagation rates along with mixed mode crack propagation rates are analysed. Finally, the conditions in order to get Mode I crack growth or shear driven propagation are discussed.     

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.     

Numerical simulations of specimen size and mismatch effects in ductile crack growth - Part I: Tearing resistance and crack growth paths

The Gurson-Tvergaard-Needleman (GTN) model has been used for detailed numerical simulations of the effects of specimen size and yield stress mismatch on ductile crack growth behaviour in two different finite specimen geometries. For deep cracked bending specimens the crack growth resistance, expressed through the far-field J, increases as the specimen size is reduced, most strongly seen in case of low hardening. An opposite effect can be seen to some extent for shallow cracked specimens loaded in tension for low and intermediate hardening. For the yield stress mismatch cases low hardening and bend loading are found to promote crack growth deviation away from the initial crack plane.     

Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation

The purpose of this work is to develop a finite element simulation of static ductile tearing tests carried out on pipeline-steel wide plates. Experiments have been presented in a companion paper (Part I [1]).The simulation is based on an extension of the Gurson–Tvergaard–Needleman model which includes plastic anisotropy and viscoplasticity effects. The parameters of the model are fitted using tensile specimens (smooth and notched bars). Simulated tests are used to evaluate macroscopic fracture parameters which were experimentally measured: the energy dissipation rate R and the thickness reduction Z.The simulation tool is then used to numerically investigate the effect of plate thickness, plastic anisotropy and through-thickness hardness gradients on the crack growth resistance. It is shown that with increasing thickness, the energy dissipation rate first increases and then decreases. A through-thickness hardness gradient is beneficial when the surface is harder than the bulk. Plastic anisotropy can be either detrimental or beneficial depending on the loading direction. These effects are explained in terms of plastic localization inducing necking along the crack path and in terms of stress distribution.     

Use of a Ring DWTT Specimen for Determination of Steel NDT from Pipe of Diameter Less than DN500

It has become recognized that the drop weight tearing test (DWTT) energy better represents the ductile fracture resistance of pipe steels since it utilizes a specimen that has the full thickness of the pipe and has a fracture path long enough to reach steady-state fracture resistance. However, the API 5L code does not require it for pipe sizes less than DN500. The aim of this paper is to propose a DWTT specific to small diameter pipes based on a new specimen, the ring drop weight tearing test (RDWTT) specimen; to evaluate the transition temperature T _{t, DWTT} and nil ductility temperature of the pipe steel API 5L X65; to introduce the transition temperature T _{t, DWTT} in the transition temperature material master curve of the API 5L X65 steel; and to compare the prediction of the crack ductile extension in a pipe based on the RDWTT’s energy and crack tip opening angle in the case of the steel API 5L X65.     

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.     

Mixed mode fracture energy of sprucewood

The characterization of Mixed Mode (Mode I and Mode II) behaviour of wood was concentrated on concepts of linear fracture mechanics in the past. Using an adopted version of the splitting test it was possible to obtain complete load displacement curves under different Mixed Mode loading cases for crack propagation along the grain. Therefore fracture energy concepts (specific fracture energy) could be used to characterize the material behaviour. Additionally strength parameters were used in order to describe crack initation in two crack propagation systems. The values for specific fracture energies as well as the strength values were compared with pure Mode I fracture tests. Moreover, the size effect under Mixed Mode loading was investigated to guarantee size independent material characterizing values for the specific fracture energies.