Influence of mixed mode I/III loading on fracture toughness of mild steel at various strain rates

Abstract

The effect of loading angle &phis; on the fracture toughness of mild steel at various strain rates has been studied. The fracture toughness was found to decrease with increasing loading angle (or increasing mode III component) at strain rates 10^-5 to 10⁰ s^-1 where ductile fracture was observed. Under impact conditions (strain rate 10² s^-1), fracture was by cleavage and the fracture toughness was found to increase with increasing loading angle. The results showed that the mixed mode fracture behaviour of mild steel changed from Class C in the strain rate range 10^-5 to 10⁰ s^-1 to a combination of Class A and B under impact conditions. In the strain rate range 10^-5 to 10^-2 s^-1, the fracture toughness behaviour with increasing strain rate was found to be similar for the three loading angles studied, namely &phis;= 0, &phis;= 30 and &phis;= 45°. At the strain rates 10^-2 to 10² s^-1, fracture toughness at &phis;= 0° decreased sharply, while for loading angles &phis;= 30° and &phis;= 45°, the fracture toughness increased with strain rate. The increase in mixed mode fracture toughness with strain rate in this strain rate regime has been attributed to the inertial effects which are known to reduce the T stress ahead of the crack.     

Investigation of proper specimen geometry for mode I fracture toughness testing with flattened Brazilian disc method

Investigation of geometrical parameters for flattened Brazilian disc method is important, since this is a simple and attractive method for mode I fracture toughness testing on rock cores. Evaluating numerical modeling results, a parametric equation in terms of principal stresses at the center of the disc and the loading angle of the flattened end was developed. An equation was proposed for maximum stress intensity factors at critical crack lengths around stable to unstable crack propagation. Comparing fracture toughness results of flattened Brazilian disc method to the results of the suggested cracked chevron notched Brazilian disc method, geometrical parameters for flattened Brazilian discs were investigated. Diameter, loading angle of flattened ends, and thickness of andesite rock core specimens were changed to obtain comparable results to the suggested method. The closest results to the suggested method were obtained by 54 mm diameter discs with loading angles larger than 32°, and thicknesses between 19 and 34 mm. Results were confirmed by the flattened Brazilian disc tests on a marble rock. In flattened Brazilian disc tests with smaller loading angles and larger diameters, larger fracture toughness values than the results of the suggested cracked chevron notched were obtained. However, excluding tests with large loading angles over 27°; specimen size was less effective on the results of these tests. Critical crack length parameters computed from modeling and experiments were close to each other for the flattened Brazilian disc specimens with smaller loading angles around 20° and thickness/radius ratio equal or less than 1.1.     

Effect of bolt clamping force on the fracture strength of mixed mode fracture in an edge crack with different sizes: Experimental and numerical investigations

To investigate the effect of bolt clamping force, resulting from torque tightening, on the mixed mode fracture (I and II) strength and effective geometry/loading factor of an edge crack with different lengths, experimental and numerical studies have been carried out. In the experimental part fracture tests were conducted on three batches of simple edge crack and bolt torque tightened with 3.5 and 7 N m edge crack at three different crack sizes of Poly methyl-methacrylate (PMMA) rectangular plate. The specimens’ fracture strength was obtained using a tensile test machine at different loading angles by employing a modified Arcan fixture. In numerical part, finite element simulations were employed to model the three test specimen batches at the three crack lengths to obtain their stress intensity geometry/loading factors. The results show that the bolt tightening torque significantly reduces the effective geometry/loading factor, and thus increases the joint fracture strength compared to bolt-less simple edge crack specimens. However, the bolt clamping effect on increasing the fracture strength was almost the same for different crack lengths.     

Determination of interfacial fracture toughness of bone-cement interface using sandwich Brazilian disks

The long-term stability of cemented total hip replacements critically depends on the lasting integrity of the bond between bone and bone cement. Conventionally, the bonding strength of bone-cement is obtained by mechanical tests that tend to produce a large variability between specimens and test methods. In this work, interfacial fracture toughness of synthetic bone-cement interface has been studied using sandwiched Brazilian disk specimens. Experiments were carried out using polyurethane foams as substrates and a common bone cement as an interlayer. Selected loading angles from 0° to 25° were used to achieve full loading conditions from mode I to mode II. Finite element analyses were carried out to obtain the solutions for strain energy release rates at given phase angles associated with the experimental models. The effects of crack length on the measured interfacial fracture toughness were examined. Microscopic studies were also carried out to obtain the morphology of the fractured interfaces at selected loading angles.The implication of the results on the assessment of fixation in acetabular replacements is discussed in the light of preliminary work on bovine cancellous bone-cement interface.     

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°.     

Analysis of the effect of biaxial loading on the fracture toughness of reactor pressure-vessel steels

The stress-strain state at the crack tip and its relation to the crack opening displacement and the J-integral under biaxial loading have been studied by solving elastoplastic problems in a geometrically nonlinear formulation by the finite-element method. Numerical investigations have been performed for various cracks and two modes of biaxial loading (tension and bending) under conditions of both small-scale and large-scale yielding. For prediction of the influence of biaxial loading on fracture toughness (at brittle fracture) a procedure has been developed that is based on established laws of stress-strain state formation at the crack tip under biaxial loading and a criterion of brittle fracture proposed earlier. The effect of biaxial loading on fracture toughness is predicted as applied to reactor pressure-vessel steels. Calculated results are compared with avilable experimental data. Alternative approaches to prediction of the effect of biaxial loading on fracture toughness are discussed. TsNII KM “Prometei,” St. Petersburg, Russia. Translated from Problemy Prochnosti, No. 5, pp. 5–26, September–October, 1999.     

Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy

The main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading.     

Experimental research on the compressive fracture toughness of wing fracture of frozen soil

It is commonly found that not only bending fracture but also compressive fracture occur frequently in compression, furthermore, in some specific conditions, compressive fracture sometimes has dominant effect on frozen soil. Therefore, it is extremely necessary to study the mechanical characteristics of the compressive fracture of frozen soil and to investigate the damage and fracture mechanism of frozen soil based on the previous research on frozen soil damage in compression. This study draws on the ideas and methods used in compression fracture research on ice that is very similar to frozen soil, and specific clay in Shenyang region was adopted as the experimental material, to make compressive specimens containing tilted wing crack of different angles, and uniaxial unconfined compression fracture experiments were conducted at different temperatures and loading rates. The fracture toughness K_IC and K_IIC of the main crack tip of the specimens are calculated with obtained experimental results and the law of K_IC and K_IIC changing with tilted angles, temperatures and loading rate is obtained to gain an insight to damage mechanism of frozen soil in compression. This paper presents a meaningful attempt for the research on compressive fracture of frozen soil, so as to better solve practical engineering problems.     

Brittle fracture in rounded-tip V-shaped notches

Two failure criteria are proposed in this paper for brittle fracture in rounded-tip V-shaped notches under pure mode I loading. One of these criteria is developed based on the mean stress criterion and the other based on the point stress criterion which both are well known failure criteria for investigating brittle fracture in elements containing a sharp crack or a sharp V-notch. To verify the validity of the proposed criteria, first the experimental data reported by other authors from three-point bend (TPB) and four-point bend (FPB) tests on PMMA at −60 °C and Alumina–7% Zirconia ceramic are used. Additionally, some new fracture tests are also carried out on the rounded-tip V-notched semi-circular bend (RV-SCB) specimens made of PMMA for various notch opening angles and different notch tip radii. A very good agreement is shown to exist between the results of the mean stress criterion and the experimental data.     

Expected position of the fatigue fracture plane by using the weighted mean principal Euler angles

The expected principal stress axes under multiaxial fatigue loading are determined by averaging the instantaneous Euler angles through suitable weight functions. Then, the fracture plane position is derived from such expected principal stress directions. Three weight functions based on stress parameters are discussed by comparing theoretical predictions with available test results related to six metallic materials under proportional and non-proportional loading. The fatigue fracture plane position under multiaxial loading may be established on the basis of the averaged direction of the maximum principal stress, with such a direction deduced by employing proper weight functions.     

High cycle fatigue and fracture mode analysis of 2A12–T4 aluminum alloy under out-of-phase axial–torsion constant amplitude loading

Fatigue experiments with solid cylindrical bar specimens are carried out to investigate the effects of stress amplitude ratios and phase angles on the axial–torsion high-cycle fatigue failure of 2A12–T4 aluminum alloy. Macro- and micro-analysis of the specimen fracture appearance is conducted in order to obtain the fracture characteristics under combined axial–torsion loading with different stress amplitude ratios and different phase angles. The soft factor of fatigue loading is introduced to estimate the failure mode under the combined axial–torsion loading. The result indicates that the estimation about the soft factor of fatigue loading is consistent with the macro- and micro-analysis.     

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

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Interfacial fracture of dentin adhesively bonded to quartz-fiber reinforced composite

The paper presents the results of an experimental study of interfacial failure in a multilayered structure consisting of a dentin/resin cement/quartz-fiber reinforced composite (FRC). Slices of dentin close to the pulp chamber were sandwiched by two half-circle discs made of a quartz-fiber reinforced composite, bonded with bonding agent (All-bond 2, BISCO, Schaumburg) and resin cement (Duo-link, BISCO, Schaumburg) to make Brazil-nut sandwich specimens for interfacial toughness testing. Interfacial fracture toughness (strain energy release rate, G) was measured as a function of mode mixity by changing loading angles from 0° to 15°. The interfacial fracture surfaces were then examined using Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDX) to determine the failure modes when loading angles changed. A computational model was also developed to calculate the driving forces, stress intensity factors and mode mixities. Interfacial toughness increased from ≈ 1.5 to 3.2 J/m² when the loading angle increases from ≈ 0 to 15°. The hybridized dentin/cement interface appeared to be tougher than the resin cement/quartz-fiber reinforced epoxy. The Brazil-nut sandwich specimen was a suitable method to investigate the mechanical integrity of dentin/cement/FRC interfaces.     

Impact fracture of a ferritic steel in the lower shelf regime

This paper reports the results of a systematic investigation on the fracture of Charpy-V notch A508 steel specimens, tested in the lower shelf regime. The fracture energy has been determined for quasi-static, standard Charpy and one-point-bend impact. The results show a general trend for the fracture energy to increase with the loading rate, at the lower temperature (–160 °C). At this temperature, the roughness of the fracture surface increases markedly with the loading rate. The fractographic analysis shows the presence of 3–4 cleavage initiation sites situated at 100–800 m from the crack front, irrespective of the loading rate. Numerous cleavage microcracks are observed underneath the main fracture plane. The statistical analysis shows that the length distribution of the microcracks is adequately described by Weibull statistics. It is also found that the number of microcracks increases with the loading rate. It is suggested that the larger number of microcracks is responsible for the observed increased roughness and energy dissipation.     

Mixed-mode fracture angle and fracture locus of materials subjected to compressive loading

The incipient fracture angle and fracture loci of prenotched brittle-like material subjected to compressive loading are investigated analytically and experimentally.The analysis of the problem includes parameters whose effects on fracture were pronounced via laboratory tests, namely: notch-tip curvature, subcritical microcracks emanating from the notch and crack closure process. Such considerations, jointly with the well-established fracture criteria in tensile loading (like the critical energy release rate, the critical energy density, J-integral and critical maximum stress used in this work) yielded an associated fracture locus for each criterion. Due to the mixed mode nature of the situation (K₁ and K₂) preevaluation of the fracture angle was instrumental.Data on critical (far-field) compressive load along with measured fracture angles performed on PMMA and Tungsten Carbide specimens are used to depict the most suitable fracture locus and thus to distinguish between the various fracture criteria when extended to fracture under compressive loading. An exact expression for the threshold load for complete closure of 2D elliptical cracks is used to delimit the fracture locus.     

Quasi-static and dynamic fracture initiation toughness of Ti/TiB layered functionally graded material under thermo-mechanical loading

Quasi-static and dynamic fracture initiation toughness of Ti/TiB layered functionally graded material (FGM) is investigated using a three point bend specimen. The modified split Hopkinson pressure bar (SHPB) apparatus in conjunction with induction coil heating system is used during elevated temperature dynamic loading experiments. A simple and accurate technique has been developed to identify the time corresponding to the load at which the fracture initiates. A series of experiments are conducted at different temperatures ranging from room temperature to 800 °C, and the effect of temperature and loading rate on the fracture initiation toughness is investigated. The material fracture toughness is found to be sensitive to temperature and the fracture initiation toughness increases as the temperature increases. Furthermore, the fracture initiation toughness is strain rate sensitive and is higher for dynamic loading as compared to quasi-static loading.     

The impact behavior of aluminum alloy 6061: Effects of notch severity

In this paper the influence of notch acuity and test temperature on the impact behavior of aluminum alloy 6061 is presented and discussed. Notch angles of 45°, 60°, 75° and 90° were chosen for a standard charpy impact test specimen containing two such notches positioned at right angles to the applied load. For a given angle of the notch the dynamic fracture toughness increased with an increase in test temperature. At a given test temperature, the impact toughness of a ductile microstructure decreased with an increase in notch severity. For the least severe notch dynamic fracture surfaces revealed the occurrence of localized mixed-mode deformation at the elevated temperature. An increase in notch severity resulted in essentially Mode-I dominated fracture at all test temperatures. The results are discussed in light of alloy microstructure, fracture mechanisms and deformation field ahead of the advancing crack tip.     

Fracture of U-notched specimens under mixed mode: Experimental results and numerical predictions

The first part of the paper gives an account of 153 fracture tests on blunted notched specimens (with notches of root radius ranging from 0.3 to 4.0 mm), loaded under mixed mode (ranging from almost pure mode I to mode II, and beyond). Maximum loads and initial crack angles were measured as a function of notch root radius and loading mixity. Such results can help in evaluating numerical models of the fracture of notched components. The second part of the paper deals with the suitability of the cohesive crack concept for predicting fracture loads under mixed mode. Use of local mode I was considered for numerical computations. Comparison of experimental results with numerical predictions was significantly accurate. Diagrams of fracture loci for notched components loaded under mixed mode are discussed.     

Dynamic tensile properties of carbon fiber composite based on thermoplastic epoxy resin loaded in matrix-dominant directions

The dynamic tensile properties of carbon fiber (CF) composite loaded in the matrix-dominant direction are experimentally determined. In this study, thermoplastic epoxy resin is used as a matrix of the CF composite. A dynamic tensile test is performed using a tension-type split Hopkinson bar technique. The experimental results show that there are not linear relationships between tensile strength and strain rate in case of the 10°, 30° and 45° specimens, although the tensile strength of CF composite, whose matrix is typical thermosetting epoxy resin, linearly increases with the strain rate for all fiber orientation angles. From the fracture surface observation, it is found that the ductile fracture of the matrix can be observed only when 10° off-axis specimen is tested under dynamic loading condition. It is inferred that the softening of the thermoplastic epoxy resin in the vicinity of interface area takes place with increasing strain rate.     

The effect of mode ratio and bond interface on the fatigue behavior of a highly-toughened epoxy

The fatigue threshold and the cyclic crack growth of a highly-toughened epoxy adhesive were studied under mode I and several mixed-mode loading cases and compared with the quasi-static critical fracture energies. Four different adhesive systems were examined using steel and aluminum substrates having different surface roughness, and surface treatment. The effect of increasing the amount of mode II (increasing the phase angle) on the fatigue threshold strain energy release rate and the cyclic crack growth rate was found to be insignificant at low phase angles. However, a significant increase in the fatigue threshold and decrease in the cyclic crack growth rate was observed at higher phase angles. These trends were similar to that seen in adhesive joint fracture. Adherend surface roughness and surface preparation affected the fatigue behavior significantly, particularly at low crack speeds and high phase angles. The fatigue properties were essentially the same for both steel and aluminum adherends provided that the crack paths were cohesive. A general observation was that the fatigue crack path moved progressively closer to the more highly strained adherend under mixed-mode loading as the applied strain energy release rate and hence the crack speed, decreased. This caused mixed-mode cracks to be nearly interfacial in the threshold region.