Mean Stress Criteria Research Articles

Fracture analysis of dissimilar Al‐Al friction stir welded joints under tensile/shear loading

AbstractIn this research, fracture of dissimilar friction stir welded (FSWed) joint made of Al 7075‐T6 and Al 6061‐T6 aluminum alloys is investigated in the cracked semi‐circular bend (CSCB) specimen under mixed mode I/II loading. Due to the elastic‐plastic behavior of the welded material and the existence of significant plastic deformations around the crack tip at the propagation instance, fracture prediction of the FSWed specimens needs some failure criteria in the context of the elastic‐plastic fracture mechanics which are very complicated and time‐consuming. For this purpose, the Equivalent Material Concept (EMC) is used herein by which the tensile behavior of the welded material is equated with that of a virtual brittle material. By combining EMC with the 2 brittle fracture criteria, namely the maximum tangential stress (MTS) and mean stress (MS) criteria, the load‐carrying capacity (LCC) of the FSWed CSCB specimens is predicted. Comparison of the experimental results and theoretical predictions from the 2 criteria showed that both criteria could accurately predict the LCC of the cracked specimens. Moreover, as the contribution of mode II loading increases, the size of the plastic region around the crack tip at failure increases, leading to increasing the LCC.

Multiscale Insights Into Borehole Instabilities in High‐Porosity Sandstones

AbstractThis paper presents a multiscale analysis of the classical borehole instability problem in high‐porosity sandstones using a hierarchical multiscale approach. A rigorous, two‐way message‐passing coupling of finite element method and discrete element method is employed, where the finite element method is employed to solve a boundary value problem and the constitutive material responses required at each of its integration points are derived by the discrete element method solution to an embedded representative volume element instead of by using an assumed phenomenological model. We employ this multiscale approach to examine the successive failure of a borehole subjected to gradually decreased support stresses at the inner borehole wall or increased far‐field stresses. To reproduce the material behavior of high‐porosity sandstone, representative volume elements with a high‐porosity structure and interparticle bonds are generated. It is found that stress concentration triggers the initial failure at the borehole wall, and the subsequent failure in form of deformation bands is driven by further stress concentration ahead of the band tips. The failure pattern around the borehole varies with initial stress state and global loading path. The comparison of the local stress paths of the initial failure points in various cases reveals that the change of failure pattern from shear failure to mixed‐mode failure and to compaction failure is dominated by the increased mean stress. Cross‐scale parametric studies show that the failure mode changes from clear compaction bands to multiple arrays of shear bands by changing the high‐porosity specimen to a low‐porosity one. The increase in cohesion strength expands the yield locus and enlarges the critical mean stress between different failure patterns. Hence, the failure mode may change from compaction failure to mixed‐mode failure or from mixed‐mode failure to shear failure due purely to the increased cohesion strength. The qualitative comparisons indicate greater length, larger area, and more severe damage of the diametrically opposite failure with the increase in minor principal stress σ0 and principal stress ratio. The diametrically opposite failure mode is found a good indicator for σ0 direction, but it may also occur under hydrostatic far‐field stress due to material anisotropy.

Fracture study in notched ductile polymeric plates subjected to mixed mode I/II loading: Application of equivalent material concept

Abstract Fracture of a ductile polymeric material containing U-notches is studied both experimentally and theoretically under mixed mode I/II loading conditions. Rectangular plates containing a central bean-shaped slit with two U-shaped ends are utilized for conducting fracture tests. Specimens with different notch inclination angles and various notch tip radii are loaded under remote tension to measure their load-carrying capacities (LCCs) experimentally. The Equivalent Material Concept (EMC) is reformulated to be utilized for theoretically predicting the obtained experimental results. For this purpose, the maximum tangential stress (MTS) and the mean stress (MS) criteria are combined with EMC. As the main novelty of this research, it is revealed that both the EMC-MTS and EMC-MS criteria, which have been more recently used for studying only pure mode I fracture behavior of U-notched epoxy resin, can provide very good predictions to the experimental results obtained under mixed mode I/II loading conditions.

Fracture study of a ductile polymer-based nanocomposite weakened by blunt V-notches under mode I loading: Application of the Equivalent Material Concept

The onset of fracture is studied in a ductile epoxy-based nanocomposite containing round-tip V-notches both experimentally and theoretically under pure mode I loading conditions. Mechanical properties of the nanocomposite containing 0.1, 0.3, 0.5 and 1 wt% multi-walled carbon nanotubes (MWCNTs) are experimentally measured to find a desired amount of nanoparticles. Rectangular plates containing a central rhombic hole with four blunt V-shaped corners are utilized as the samples for fracture tests. Specimens with two different notch angles of 30° and 60° and various notch tip radii are tested under remote tension to obtain their load-carrying capacities (LCCs) experimentally. For theoretically predicting the experimental results, the Equivalent Material Concept (EMC) is reformulated and utilized. Two well-known brittle fracture criteria, namely the maximum tangential stress (MTS) and the mean stress (MS) criteria, are employed in conjunction with EMC for theoretical predictions. It is revealed that both the EMC-MTS and EMC-MS criteria could predict the experimental results well, without performing any elastic-plastic analyses of the nanocomposite specimens.

A threshold formula for fatigue crack growth with mean stress intensity factors

From the fatigue limit condition of crack front, a threshold formula has been derived with respect to mean stress intensity factors. Examinations with experimental results show that this formula can express threshold quantitatively and uniformly. It is found that threshold varies with mean stress intensity factor just as that fatigue limit varies with mean stress if the mean stress intensity factor is smaller than a critical value, while if the mean stress intensity factor is larger than the critical value, plastic deformation at crack front would affect threshold greatly. It has also been investigated that why there would be such a critical mean stress intensity factor behavior. The reason lies on that whether damage induced by plastic deformation at crack front could be neglected or not. A formula to estimate the critical mean stress intensity factor has also been derived.

Experimental and theoretical investigation of mixed mode I/III brittle fracture of U-notched polystyrene components

Brittle fracture of components made of the general-purpose polystyrene and weakened by an edge U-notch under combined tension/out-of-plane shear loading conditions (mixed mode I/III) has not been studied yet experimentally or theoretically. In this research, a recently developed loading fixture is employed for experimentally investigating the fracture of U-notched general-purpose polystyrene samples with various notch tip radii of 0.5, 1, 2 and 4 mm when they are subjected to different combinations of tension/out-of-plane shear. The samples are fabricated with four different notch tip radii with the purpose of assessing the influence of this geometrical parameter. The experimental values of fracture load and out-of-plane fracture angle are theoretically predicted by the two stress-based criteria of point stress and mean stress lately extended to general loading case of mixed mode I/II/III. It is shown that both the point stress and mean stress criteria provide acceptable predictions to fracture behavior of U-notched general-purpose polystyrene specimens. The critical distances needed for the point stress and mean stress criteria are determined based on the experimental results of the U-notched samples tested under pure mode I loading. No meaningful difference is found between the fracture loads and fracture initiation angles predicted by the point stress and mean stress criteria. It is also observed that as the mode III contribution in the applied mixed mode I/III loading increases, a larger total external load is needed for the fracture of U-notched general-purpose polystyrene specimens to occur.

Tensile fracture analysis of a ductile polymeric material weakened by U-notches

Fracture of a ductile epoxy polymer containing U-notches was investigated both experimentally and theoretically under pure opening mode. Two various U-notched polymeric specimens with different notch tip radii were utilized in the experiments; one of them was loaded under remote tension and the other under three-point bending. The load-carrying capacities (LCCs) of the U-notched polymeric specimens were experimentally recorded. To predict the experimentally obtained LCCs, the Equivalent Material Concept (EMC), proposed originally by the first author, was reformulated for the ductile polymer tested. Then EMC was linked to two well-known brittle fracture criteria, namely the maximum tangential stress (MTS) and mean stress (MS) criteria. It is shown that both the EMC-MTS and EMC-MS criteria predict the experimental results well without needing elastic-plastic analyses of the polymer specimens.

Experimental verification of two stress-based criteria for mixed mode I/III brittle fracture assessment of U-notched components

In the present study, a series of fracture experiments are conducted on PMMA U-notched samples using an improved loading configuration, which is redesign of the apparatus recently presented for doing fracture tests under combination of tensile and out-of-plane shear loading. In order to assess the effect of notch tip radius, the tested specimens are fabricated with three different radii. Two brittle fracture criteria, namely the point stress (PS) and mean stress (MS), are employed to estimate the fracture resistance and the out-of-plane angle of fracture onset of the experiments. These criteria have previously been extended to general loading type of mixed mode I/II/III for studying fracture in engineering components containing blunt V-notches. Consequence of comparing the theoretical and experimental results for different notch tip radii reveals that both criteria are accurate enough to predict the fracture behavior of the U-notched engineering members subjected to mixed mode I/III loading. It is not found any considerable difference between the curves of fracture initiation angle and fracture resistance resulted from the PS and MS criteria. The criteria also show that the out-of-plane fracture angle due to pure mode III loading is constant and independent of the notch tip radius.

Large plasticity induced crack initiation from U-notches in thin aluminum sheets under mixed mode loadin

Article history: Received 6 July, 2016 Accepted 2 October 2016 Available online 3 October 2016 Ductile failure is investigated experimentally and theoretically in U-notched Al 7075T6 thin sheets under mixed mode I/II loading. First, several U-notched rectangular sheets are subjected to mixed mode I/II failure tests and the load-carrying capacity of the sheets are experimentally recorded. Then, the Equivalent Material Concept (EMC) is employed in conjunction with the U-notch maximum tangential stress (UMTS) and U-notch mean stress (UMS) criteria to theoretically estimate the load-carrying capacity of the U-notched Al 7075-T6 sheets. It is shown that the experimental failure loads are well predicted by means of both the UMTS-EMC and UMS-EMC criteria. Moreover, the experimental observations and the elastic-plastic finite element analyses indicate that the U-notched aluminum sheets fail by the large-scale yielding (LSY) regime. © 2017 Growing Science Ltd. All rights reserved.

Brittle failure of key-hole notches under mixed mode I/II loading with negative mode I contributions

Brittle failure of key-hole notches is investigated experimentally and theoretically under mixed mode I/II loading with negative mode I contributions. The key-hole notched Brazilian disk specimen made of the general-purpose Polystyrene is utilized for conducting the fracture experiments. To predict the experimental results, the key-hole notch maximum tangential stress and key-hole notch mean stress criteria are utilized. It is shown that both criteria could provide good predictions to the experimental results of the fracture load. Moreover, the key-hole notch mean stress criterion with the experimentally determined critical distance is shown to be the most accurate failure criterion.

Mixed mode I/II brittle fracture in V-notched Brazilian disk specimens under negative mode I conditions

The well-known round-tip V-notched Brazilian disk specimen is utilized for conducting mixed mode I/II fracture tests on PMMA under negative mode I conditions for different notch angles and various notch radii with the aim to measure experimentally the fracture load and the fracture initiation angle. It is shown by the finite element analysis that although the notch is under negative mode I loading, one side of the notch border still experiences tensile tangential stresses suggesting that fracture would take place from the same side of notch border. Experimental observations also indicated that fracture occurs from the tensile side of the notch border confirming the finite element results. The experimental results are then theoretically estimated by means of two stress-based brittle fracture criteria, namely the round-tip V-notch maximum tangential stress and the mean-stress criteria. It is shown that both criteria provide very good predictions to the experimental results obtained under negative mode I conditions.

Numerical Modelling of AISI 316L Cardiovascular Stent Behaviour under Blood Pressure and Restenosis Loadings

In the present study, ABAQUS finite element modelling was used to explore the durability of cardiovascular stent made of AISI 316L. It was found that the blood pressure loading never causes the fracture of the stent. This result was confirmed by the application of two critical plane approaches and one mean stress criterion. However, when subjected to restenosis compressive loading the stent was found to experience an in-service failure. The last proved to be dependent on the stent diameter reduction, rate and location of restenosis. Since restenosis forms gradually and randomly within the artery, two distributions were considered and investigated. The eccentric restenosis turned out to be more deleterious than the concentric one.

Application of the equivalent material concept to ductile failure prediction of blunt V-notches encountering moderate-scale yielding

The equivalent material concept, proposed originally by the first author for predicting tensile load-carrying capacity of ductile metallic materials weakened by V-notches, was employed together with two well-known brittle fracture criteria, namely the point-stress and the mean-stress criteria, to estimate theoretically the tensile load-carrying capacity of rectangular plates made of Al 7075-T6 and weakened by blunt V-notches encountering moderate-scale yielding at failure. With average discrepancies of 12.4 and 9.7%, it was found that both the equivalent material concept–point-stress and the equivalent material concept–mean-stress criteria could provide satisfactory predictions to the experimental results. Also, found in this research was that for large notch radii, the equivalent material concept–point-stress criterion could predict the test results better than the equivalent material concept–mean-stress criterion and vice versa.

Mixed mode I/III brittle fracture in round-tip V-notches

Two stress-based failure criteria, presented in the past to study brittle fracture in engineering components weakened by a blunt V-notch under mixed mode I/II loading, are extended in the present study to general mixed mode I/II/III loading. As a reduced case, two brittle fracture criteria are developed for mixed mode I/III loading conditions based on the two well-known failure concepts of the maximum tangential stress (MTS) and the mean-stress (MS) which both have been frequently used for predicting mixed-mode I/II brittle fracture in notched components. In order to verify the validity of the criteria, the theoretical predictions are compared with a bulk of new experimental results recently reported in the open literature on mixed-mode I/III fracture of round graphite bars weakened by circumferential blunt V-notches. The results of the criteria are represented in the form of fracture curves in terms of the notch stress intensity factors. Good agreement is shown to exist between the mixed-mode I/III results of the MS criterion and the experimental results for different notch tip radii and various notch opening angles. Conversely, the results show that the MTS criterion provides weaker estimates compared to the MS criterion.

Mixed-mode ductile failure analysis of V-notched Al 7075-T6 thin sheets

First, several rectangular thin sheets made of Al 7075-T6 and weakened by blunt V-notches were tested for mixed mode I/II fracture, and the load-carrying capacity and the fracture initiation angles were experimentally recorded. Then, the Equivalent Material Concept (EMC), proposed originally by the first author, was utilized in conjunction with the maximum tangential stress (MTS) and the mean-stress (MS) criteria to predict the experimental results. By approximately 9% and 6.5% discrepancies for the VMTS-EMC and VMS-EMC criteria, respectively, it was found that both criteria could predict successfully the mixed-mode ductile fracture of Al 7075-T6 thin sheets without performing elastic–plastic analyses.

On the Ability of the Equivalent Material Concept in Predicting Ductile Failure of U-Notches under Moderate- and Large-Scale Yielding Conditions

In the present research, first, the equivalent material concept (EMC), proposed originally by the first author to equate a ductile material with a virtual brittle material, was utilized in conjunction with two stressbased brittle fracture criteria, namely the point-stress (PS) and the mean-stress (MS) criteria, to develop two combined failure criteria capable of predicting tensile crack initiation from U-notches in ductile materials. Then, to verify the two failure criteria, several rectangular thin plates weakened by a central bean-shaped slit with two U-shaped ends and made of aluminum alloys Al 7075-T6 and Al 6061-T6 were tested under tension. Experimental observations indicated that Al 7075-T6 plates failed by moderate-scale yielding while Al 6061-T6 by largescale yielding. It was found that the EMC-MS criterion could predict the experimental results of both materials successfully. Meanwhile, the EMC-PS criterion was found to be accurate for moderate and large notch radii, particularly for Al 6061-T6 material.

Brittle fracture analysis of blunt V-notches under compression

Brittle fracture was investigated both experimentally and theoretically in blunt V-notches under compression. A new test specimen, called flattened V-notched semi-disk (FVSD) specimen, was suggested for conducting fracture tests on PMMA under compression for different notch angles and various notch radii with the aim to measure experimentally the compressive notch fracture toughness. The experimental results were theoretically estimated by means of two stress-based brittle fracture criteria, namely the point-stress (PS) and the mean-stress (MS) criteria. With total accuracies of 91% and 90% for the PS and the MS criteria, respectively; it was found that both the criteria provide very good predictions to the experimental results.

Mode II notch fracture toughness measurement for key-hole notches by the disk test

A new version of the well-known Brazilian disk specimen weakened by a dumbbell-shaped slit with two key-shaped ends, called key-hole notched Brazilian disk specimen, made of polymethylmethacrylate, was utilized to measure experimentally the notch fracture toughness for key-hole notches of various radii and different lengths under pure mode I and pure mode II loading conditions. The experimental values of the mode II notch fracture toughness/mode I notch fracture toughness ratio were theoretically estimated by means of two brittle fracture criteria, namely, the maximum tangential stress and the mean stress criteria. Two groups of critical distances were used in the criteria. The first one was equal to that for sharp crack and the second one was directly determined from the mode I fracture tests. It was found that while both the criteria could estimate the experimental results satisfactorily, the agreement between the theoretical and the experimental results is excellent when one deals with larger notch lengths. Also found in the research was that choosing any of the critical distance groups did not affect the theoretical predictions significantly, meaning that the critical distances of sharp crack could be used in fracture prediction of key-hole notches.

Mechanics of dynamic fracture in notched polycarbonate

Fracture toughness of brittle amorphous polymers (e.g. polymethyl methacrylate (PMMA)) has been reported to decrease with loading rate at moderate rates and increase abruptly thereafter to close to 5 times the static value at very high loading rates. Dynamic fracture toughness that is much higher than the static values has attractive technological possibilities. However, the reasons for the sharp increase remain unclear. Motivated by these observations, the present work focuses on the dynamic fracture behavior of polycarbonate (PC), which is also an amorphous polymer but unlike PMMA, is ductile at room temperature. Towards this end, a combined experimental and numerical approach is adopted. Dynamic fracture experiments at various loading rates are conducted on single edge notched (SEN) specimens with a notch of radius 150μm, using a Hopkinson bar setup equipped with ultra high-speed imaging (>105fps) for real-time observation of dynamic processes during fracture. Concurrently, 3D dynamic finite element simulations are performed using a well calibrated material model for PC. Experimentally, we were able to clearly capture the intricate details of the process, for both slowly and dynamically loaded samples, of damage nucleation and growth ahead of the notch tip followed by unstable crack propagation. These observations coupled with fractography and computer simulations led us to conclude that in PC, the fracture toughness remains invariant with loading rate at Jfrac=12±3kN/m for the entire range of loading rates (J̇) from static to 1×106kN/m−s. However, the damage initiation toughness is significantly higher in dynamic loading compared to static situations. In dynamic situations, damage nucleation is quickly followed by initiation of radial crazes from around the void periphery that initiate and quickly bridge the ligament between the initial damaged region and the notch. Thus for PC, two criteria for two major stages in the failure process emerge. Firstly, a mean stress based defect initiation is suggested. The value of the critical mean stress for defect initiation under dynamic loading is found to be 115±5MPa, which is significantly higher than its static value of 80MPa. The critical normal plastic stretch needed for crazes to nucleate from the nucleated defect is estimated to be about 1.78±0.2.

Theoretical and experimental investigation of brittle fracture in V-notched PMMA specimens under compressive loading

The aim of the present investigation was twofold. First, to prepare a new set of experimental data on brittle fracture of blunt V-notches under compression and second to develop stress-based criteria for predicting the compressive notch fracture toughness of blunt V-notches. A new test specimen, called V-notch stepped cottage (VSC) specimen, made of PMMA was proposed to perform fracture experiments under compression. Two brittle fracture criteria, namely the point-stress (PS) and the mean-stress (MS) criteria, were also developed to estimate the experimental results. It was demonstrated that the experimental results could be satisfactorily predicted by using the two criteria.