Combined Axial-torsional Loading Research Articles

Prediction of surface crack growth life for AA7075-T6 under nonproportional loading

The growth direction and growth rate of fatigue cracks initiated from the surface of an aluminum alloy 7075-T6 plate were investigated under six sets of nonproportional loadings produced by combined axial-torsion loading. A digital image correlation method was simultaneously applied to measure the crack opening displacements around the crack tip during the fatigue tests. The effective stress intensity factor ranges were determined on the basis of the measured crack opening displacements and applied to arrange the crack growth rate. Results showed that fatigue crack tended to propagate orthogonally to the direction in which the resultant normal stress in the nonproportional loading cycle was maximized, suggesting that the maximum resultant normal stress dominates crack growth under nonproportional loadings. When the effective stress intensity factor range based on the maximum resultant normal stress was used to arrange the crack growth rates, all data collapsed into a single narrow scatter band. The growth lifetime until the surface crack penetrates the plate could be estimated within a relative error of about ± 20 % based on a modified Paris-type equation through numerical integration.

An Experimental Investigation of the Influence of the State of Stress on the Ductile Fracture of 2024-T351 Aluminum

Abstract This paper investigates the influence of stress state on the equivalent plastic fracture strain in 2024-T351 aluminum alloy. Eighteen unique stress states at failure—with triaxialities ranging from 0.388 (compressive) to −0.891 (tensile) and Lode parameters ranging from −0.978 to 1.000—are explored through mechanical experiments on 2024-T351 aluminum specimens with various geometries under multiple loading conditions. These include tension tests of plane stress (thin), plane strain (thick), and axisymmetric specimens, as well as pure shear and combined axial–torsional loading on thin-walled tubes. Using a hybrid numerical–experimental approach, the dependence of fracture strain on stress triaxiality and Lode parameter is quantified for each experiment. Fracture strains are measured using three-dimensional digital image correlation. Equivalent plastic fracture strain for 2024-T351 generally increases with stress triaxiality (moving toward a more compressive state). Fracture strain decreases modestly as the Lode parameter decreases from 1 to 0, although there is a significant increase in ductility as the Lode parameter decreases below −0.8. Compression–torsion tests extend the data’s stress-space coverage well into the compressive triaxiality region (up to 0.388) and to Lode parameters approaching −1. This experimental program provides the most extensive set of ductile fracture data from a single 12.7-mm-thick 2024-T351 aluminum plate in the literature. These data can be used to calibrate ductile fracture models used in finite element simulations of dynamic events such as bird strikes, automotive collisions, and debris containment.

An experimental study of the mechanical behavior of rolled AZ31B magnesium alloy under combined axial-torsion loading

The mechanical behavior and microstructure at fracture of a rolled AZ31B magnesium alloy were experimentally investigated using tubular specimens subjected to combined axial-torsion loading with different ratios of the axial and shear stress components. The stress state influences the stress-strain responses. The equivalent stress-equivalent plastic strain curves under tension-torsion loading show a sigmoidal shape and the peak value of the equivalent strain hardening rate increases as the ratio of the axial stress to the shear stress increases. Under compression-torsion, the equivalent stress-equivalent plastic strain curves show a concave-down shape, and the equivalent strain hardening rate decreases at faster rates as the ratio of the axial stress to the shear stress increases. Among all the loading conditions investigated, pure tension and pure compression result in the highest strength, and torsion combined with a slight tension has the lowest strength. The trend of ductility is inversely proportional to the strength with respect to the influence of the combined axial-torsion loading. Detailed twinning structures reveal that extensive tension twins are induced under tension-torsion loading paths. Conversely, a combination of tension and compression twins is observed under compression-torsion loading due to the high Schmid factors of the compression twins resulted from the grains with favorable orientations. The significant effect of the stress state on the post-fracture texture is explained in terms of the twin variant favorability which is dominated by the crystal orientation relative to the orientation of the applied principal stresses. The experimental results are critical for the development and validation of constitutive models for magnesium alloys under multiaxial loading.

Growth Life Prediction of Surface Crack for A7075 Aluminum Alloy under Nonproportional Loading

The growth direction and growth rate of fatigue cracks initiated from the surface of A7075 aluminum alloy plate were investigated under 6 sets of nonproportional loadings produced by the combined axial-torsion loading. The digital image correlation method was simultaneously applied to measure the crack opening displacements around the crack tip during the fatigue tests. Fatigue crack tended to propagate orthogonally to the direction in which the resultant normal stress in the nonproportional loading cycle was maximized, suggesting that the maximum resultant normal stress dominate crack growth under nonproportional loadings. The growth lifetime until the surface crack penetrates the plate could be estimated with an accuracy of about 20% based on the modified Paris-type equation through numerical integration.

Comparison of Suture-Button Fixation with Suture-Tape Augmentation and Trans-Syndesmotic Screw Fixation for Syndemosis Injury: A Biomechanical Study

Category:Ankle; Basic Sciences/BiologicsIntroduction/Purpose:The treatment of syndesmotic injuries with ankle fractures is controversial. The purpose of this study was to compare the biomechanical properties of suture-button fixation with suture-tape augmentation with those of screw fixation.Methods:Ten matched pairs of human cadaver specimens were subjected to suture-button fixation with suture-tape augmentation or screw fixation. Each specimen underwent initial intact physiologic loading, consisting of 10 cycles of axial loading with peak of 750N, 10 cycles of external torsional loading with peak of 7.5Nm, and 10 cycles of combined axial and external torsional loading with peak of 750N and 7.5Nm at 0.05 Hz. Injuries of the anterior inferior tibiofibular ligament, tibiofibular interosseous membrane, posterior tibiofibular ligament and medial malleolar fracture were applied to each specimen. Postfixation cyclic loading consisted of 50 cycles of combinedaxial and external rotation loading with peak torques of 750 N and 7.5 Nm at a rate of 0.05 Hz. After postfixation loading, each specimen underwent failure loading by external rotation at 0.25 degrees/second. Failure torque and failure angle were measured.Results:Mean failure torques were 15.99 +- 8.88 Nm in the suture-button fixation with suture-tape augmentation and 17.10 +- 10.38 Nm in the screw group. There was no significant difference in average failure torque between two groups (p-value = 0.669)Average failure angle in screw-fixation group (39.37 +- 10.19 deg) was significantly lower than average failure angle suture- button fixation with suture-tape augmentation (56.64 +- 9.64 deg) (p-value = 0.001).Average rotational stiffness in screw-fixation group (0.53 +- 0.24 Nm/deg) was significantly higher than average rotational stiffness in suture-button fixation with suture-tape augmentation group (0.35 +- 0.19 Nm/deg) (p-value = 0.033).Conclusion:Suture-button fixation with suture-tape augmentation for ankle syndesmotic injury provides similar torsional strength to that of screw fixation and has lower stiffness than screw fixation. Therefore, Suture-button fixation with suture-tape augmentation can be considered as an alternative treatment option for syndesmosis injury.

Fracture reduction has a dominant effect over cerclage wiring in increasing stiffness of intertrochanteric OTA/AO 31-A3.1 (reverse oblique) fractures managed with cephalomedullary osteosynthesis.

Objectives:To investigate the mechanical properties of cephalomedullary nailing of intertrochanteric OTA/AO 31-A3.1 (reverse oblique) fractures and to test the hypothesis that anatomical reduction and augmentation with cerclage wire produces a more stable construct.Methods:A standardized fracture model in composite saw bone was created to stimulate an intertrochaneric 31-A3.1 fracture, using a 3D printed cutting guide. Simulated osteosynthesis was performed with 12 femurs divided into anatomically reduced and varus malreduced groups. Each femur was tested with and without cerclage wire augmentation. All femurs were fixed with a 215 mm, 130 degree, 11.5 mm nail. An Instron 8874 biaxial materials testing machine was used to assess the axial stiffness. Cyclic loading consisted of 5000 cycles of sinusoidal combined axial-torsion loading at 3 Hz. Axial load was 100 N to 2000 N and torsion −4.5 Nm to +4.5 Nm. Stiffness was measured before and after cyclic loading.Results:Reduced constructs were stiffer than residual varus constructs. The mean overall fracture stiffness was 508.7 N/mm for reduced constructs and 379.2 N/mm for varus constructs. Removing the cables significantly decreased the fracture stiffness for both constructs (mean difference 60.0 N/mm, 95% CI 7.7–112.3, P = .032).Conclusions:Anatomical reduction has a dominant effect on facture stiffness. Anatomically reduced fractures are stiffer than varus malreduced fractures. A cerclage wire further improves construct stiffness if anatomical reduction is achieved. Cerclage wiring is less effective if anatomical reduction is not achieved.

Experimental study of the low-cycle fatigue life under multiaxial loading of aluminum alloy EN AW-2024-T3 at elevated temperatures

This paper presents the results of an experimental study conducted on technical aluminum alloy EN AW-2024-T3 specimens under multiaxial low-cycle-fatigue loading at elevated temperatures. An original experimental setup, consisting of a biaxial servo-hydraulic MTS 858 MiniBionix material testing system, Maytec resistance furnace, high-temperature MTS extensometer and hydraulic grips of original design, was used in tests. Tubular specimens were subjected to multiaxial fatigue loading, proportional and non-proportional (with phase shift), under isothermal conditions of the air atmosphere. Multiaxial tests were performed under combined axial-torsional loading. Fractography analysis were conducted on the tested samples, and crack initiation mechanism under conditions of multiaxial loads at elevated temperatures were identified. Obtained fatigue life values were analyzed, particularly from the perspective of the possibility of approximating them by means of simple relations.

Fatigue life and early cracking predictions of extruded AZ31B magnesium alloy using critical plane approaches

The Smith–Watson–Topper (SWT) criterion, the Fatemi–Socie criterion, and the Jiang criterion were evaluated based on the experimentally observed cracking behavior and fatigue life of an extruded AZ31B magnesium alloy. The fatigue experiments were performed on thin-walled tubular specimens subjected to tension–compression, torsion, and combined axial–torsion loading. The SWT criterion fails to correlate the tension–compression and torsion baseline experiments. The Fatemi–Socie criterion predicts well the fatigue lives for all experiments, but the criterion yields a less satisfactory prediction of the cracking behavior for most of the tests. The difficulty of the SWT and Fatemi–Socie criteria in correlating the observed cracking orientations is attributed to the mixed cracking behavior of the material. The Jiang criterion provides a reasonable description of the cracking behavior and fatigue life predictions. A discussion on the current capability of the critical plane approaches to predict the fatigue behavior of wrought magnesium alloys is presented, and further studies are recommended.

Testing and assessment of fatigue life prediction models for Indian PHWRs piping material under multi-axial load cycling

In the present paper, experimental and analytical fatigue studies on primary piping material of Indian PHWRs, have been carried out under multi-axial loading with an aim to assess the adequacy of currently used fatigue life models based on ASME B&PV Sec-III procedure and plastic strain energy density. The experiments were conducted under axial, torsion and combined axial–torsion loading with different loading waveforms, phase angle and strain ratio (shear to axial). The tests under varying principal directions loading resulted in shorter fatigue lives. The orientations of crack initiation plane were measured and found dependent on the loading parameters which supports the idea of critical plane based fatigue models.

Anisotropic yield criteria in σ–τ stress space for materials with yield asymmetry

In this study, yield behavior of an extruded magnesium alloy is investigated experimentally and analytically. A precise definition of yield is established for the extruded AZ31 magnesium alloy by deforming several specimens to certain levels of strain and measuring the residual strains after unloading. The material is then subjected to different loading conditions (uniaxial to multiaxial) at four different plastic strains. Multiaxial loading is comprised of free-end torsion and combined axial-torsion loading. Therefore, yield response is measured in σ–τ space. Several yield criteria are studied to predict yield response of extruded AZ31. The developed model by Cazacu et al. (2006), CPB06, which uses a fourth-order linear transformation, is calibrated through optimization of initial guesses. Despite the reasonable accuracy of CPB06 in prediction of experimental results, it shows that its precision significantly depends on initial guesses, which make the calculation complicated and time consuming. The asymmetrical quadratic model developed by Khan et al. (2012) presents a less accuracy in prediction of yield response of the highly textured AZ31. This study proposes an asymmetrical fourth-order polynomial yield function. Unlike CPB06, material constants in this model can be directly calculated using mechanical measurements. Convexity of the proposed model is discussed, and the domains of variation for the material parameters such that convexity holds are determined.

A new form of equivalent stress for combined axial–torsional loading considering the tension–compression asymmetry of polymeric materials

A concise form of equivalent stress which considers the tension–compression asymmetry of polymeric materials is proposed. It is more suitable for combined axial–torsional loading.

Coupled rate-dependent superelastic behavior of shape memory alloy bars induced by combined axial-torsional loading: a semi-analytic modeling

In this article, the coupled thermomechanical response of superelastic shape memory alloy bars and tubes in combined tension and torsion is studied both analytically and experimentally. Using the Gibbs free energy as the thermodynamic potential and choosing appropriate internal state variables, a three-dimensional phenomenological macroscopic constitutive model for shape memory alloys is derived. Taking into account the effect of latent heat during the forward and reverse martensitic phase transformation, the appropriate form of the energy balance relation is obtained. The three-dimensional coupled relations for the energy balance in the presence of the internal heat flux and the constitutive equations are reduced to a two-dimensional form for the tension-torsion case. An explicit finite difference approach is utilized to discretize the governing boundary conditions of bars. An empirical expression for the free heat convection from the surface of a shape memory alloy bar was proposed and experimentally va...

A modified intramedullary nail interlocking design yields improved stability for fatigue cycling in a canine femur fracture model

Intramedullary nailing has evolved to become the standard of care for most diaphyseal femoral and tibial fractures, as well as an expanding number of metaphyseal fractures. Owing to the unstable nature of some fractures, the intramedullary device may be subjected to significant stresses owing to a lack of solid cortical contact after nailing. In such cases, excessive interfragmentary motion (due to construct toggle) has been shown to occur. Such motion increases the likelihood of a non- or delayed-union. In the current study, two versions of a modified, angle stable interlocking design were subjected to fatigue testing in a segmental defect fracture model representing a canine femur. As a control, a third group of constructs were stabilized with a traditional nail that allowed a small amount of toggle. All constructs were subjected to 50,000 fatigue cycles representing 12 weeks of cage activity at physiologic levels of combined axial-torsional loading. Torsional testing pre- and post-fatigue revealed 4.6 +/- 1.3 degrees of toggle in the traditional nail and no toggle with the angle stable nail designs. The stable nails were also significantly stiffer in axial compression and torsion before and after cycling. These data indicate that the enhanced stability of the modified interlocking designs can be maintained throughout fatigue cycling in a challenging fracture model.

Multiaxial fatigue of extruded AZ31B magnesium alloy

Multiaxial fatigue behavior of extruded AZ31B magnesium alloy was experimentally studied in ambient air under strain-controlled axial-torsion loading using tubular specimens. Four fully reversed loading paths were employed: tension–compression, pure torsion, proportional axial-torsion, and 90° out-of-phase nonproportional axial-torsion. Tension–compression asymmetry in cyclic plastic deformation was observed for tension–compression and combined axial-torsion loading. For the same equivalent strain amplitude, the 90° out-of-phase nonproportional loading path resulted in the shortest fatigue life and the proportional loading path produced the longest fatigue life. Two critical plane multiaxial fatigue models, namely, the modified Smith–Watson–Topper (SWT) model and the Jiang multiaxial fatigue criterion, were evaluated based on the experimentally obtained fatigue results. Both models were found to be able to correlate the fatigue experiments reasonably well.

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.

An experimental study of cyclic deformation of extruded AZ61A magnesium alloy

Thin-walled tubular specimens were employed to study the cyclic deformation of extruded AZ61A magnesium alloy. Experiments were conducted under fully reversed strain-controlled tension–compression, torsion, and combined axial–torsion in ambient air. Mechanical twinning was found to significantly influence the inelastic deformation of the material. Cyclic hardening was observed at all the strain amplitudes under investigation. For tension–compression at strain amplitudes higher than 0.5%, the stress–strain hysteresis loop was asymmetric with a positive mean stress. This was associated with mechanical twinning in the compression phase and detwinning in the subsequent tension phase. Under cyclic torsion, the stress–strain hysteresis loops were symmetric although mechanical twinning was observed at high shear strain amplitudes. When the material was subjected to combined axial–torsion loading, the alternative occurrence of twinning and detwinning processes under axial stress resulted in asymmetric shear stress–shear strain hysteresis loops. Nonproportional hardening was not observed due to limited number of slip systems and the formation of mechanical twins. Microstructures after the stabilization of cyclic deformation were observed and the dominant mechanisms governing cyclic deformation were discussed. Existing cyclic plasticity models were discussed in light of their capabilities for modeling the observed cyclic deformation of the magnesium alloy.

Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures

An analysis-based approach for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately account for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite element analyses. The imperfection signature represents a first-approximation mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. These shapes include the actual measured imperfection shape of the test specimens, a first-approximation mean imperfection shape, with and without plus or minus one standard deviation, and the linear-bifurcation-mode imperfection shape. In addition, buckling interaction curves for composite shells subjected to combined axial compression and torsion loading are presented that were obtained by using the various imperfection shapes in the analyses. A discussion of the nonlinear finite element analyses is also presented. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates and to reduce the weight and cost of developing buckling-resistant shell structures.

An endochronic model of yield surface accounting for deformation induced anisotropy

Abstract In this article, an endochronic model of yield surface is proposed. Based on this model, the yield surface is simulated such that the forward and rear parts of the yield surface are described by different ellipses which are characterized by corresponding aspect ratio functions, respectively. Verification of the endochronic theory used the experimental results of yield surfaces obtained by Wu and Yeh for 304 stainless steel (Wu, H.C., Yeh, W.C., 1991. On the experimental determination of yield surfaces and some results of annealed 304 stainless steel. Int. J. Plasticity 7, 803–826). The experiments were performed cyclically under uniaxial, torsional, and combined axial–torsional loading conditions. The result has shown that the agreement between the prediction and experiments is quite satisfactory. In addition to the distortion of the yield surface plastically behaving a sharp front accompanied by a blunt rear, the anisotropic kinematic hardening effect has been addressed in this investigation. Although the experimental results of yield surfaces subjected to non-proportional loading conditions can be found in the literature, lack of information about the plastic strain history makes it impossible to verify the theory under such complicated loading conditions. The domain of applicability and validity of the theory, which is defined in terms of plastic strain increments, need be further investigated with the aim to set up related experiments.

A study of loading path influence on fatigue crack growth under combined loading

Single edge specimens made of 1070 steel were subjected to combined axial–torsion loading at room temperature. Three loading paths were designed to study the loading path influence on the crack growth behavior. Path I was proportional loading and Path II was the loading case, where the torque decreased/increased with increasing/decreasing axial load. Path III followed a circular path in the axial load–torque coordinates. With identical load amplitudes, the crack growth behavior was found to be critically dependent on the loading path. Path III resulted in the fastest crack growth rate and Path II produced the least crack extension. Furthermore, the crack profile was dependent on the loading path. Path III resulted in a crack profile similar to that observed under Mode I loading. Significant branching and slant angles were observed for Paths I and II, with Path II in particular. Two existing models were discussed with respect to their capabilities to predict the crack growth rate and cracking direction for combined loading.

Influence of phase angle between axial and torsional loadings on fatigue fractures of bone

Fatigue fractures of cortical bone involve combined axial–torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0° and 90° phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures.