Multiaxial Conditions Research Articles

Fabric anisotropy effects on static liquefaction under constant shear drained loading

Several case history failures of slope systems have highlighted that the instability onset in loose materials can be triggered under prevailed drained conditions and stress paths that can be represented by constant shear drained (CSD) loading. This study uses the anisotropic critical state theory (ACST) to assess the effect of fabric anisotropy and loading characteristics (e.g., Lode angle and principal stress direction) on the instability onset under CSD stress paths, comparing our numerical-based observations with available experimental information. Towards this end, the ACST-based SANISAND-F model’s performance under CSD stress paths is also assessed. In addition, multiaxial conditions are incorporated through the estimation of instability surfaces. The numerical simulations are useful in explaining that the instability onset under CSD loading is dictated by a trade-off of volumetric strain components. Moreover, the results show an important effect of fabric anisotropy on the instability stress ratio (ηf). For conditions representative of common experimental setups, ηf decreases with the increase of the Lode angle and the major principal stress inclination, and ηf increases with the increase of initial fabric intensity, consistent with available experimental evidence. However, these trends can change based on the interaction between the Lode angle and loading/fabric directions; hence, departing from typical experimental observations. Finally, we discuss the potential of a simplified approach to estimate ηf analytically, including fabric effects.

Acoustic emission for identification of the dominant stress component in polymer composites at early loads

Carbon Fiber Reinforced Polymer (CFRP) composites are broadly used in engineering applications. Their inherent anisotropy due to different fiber orientations can be considered an advantage since the strength of the component can be designated in preferential loading directions. However, this anisotropy leads to multiaxial stress conditions, complicating their damage sequence and mechanical response. Identification of these multiaxial conditions at early loading stages is of paramount importance to predict the upcoming structural response of the material. Acoustic Emission (AE) is applied in this study to CFRP laminates with different stacking sequences, in which different multiaxial conditions are generated. Laminates consisting of 30o plies are characterized by dominant shear stresses, whereas in laminates with 60o layers transverse normal stresses govern the stress state. Through quasi-static and incremental loading, it is shown that certain AE features can be used to identify the dominant stress component rather than just the occurring damage mode even at early loads, before severe fracture influences the mechanical capacity. This is of great importance in cases that detrimental shear stresses are generated, leading to delaminations and mechanical deterioration. AE can be used in this direction to predict the upcoming damage and to take necessary measures to avoid final failure.

An improved continuous damage model to estimate multiaxial fatigue life under strain control problems

In this contribution, a modification and application of the Lemaitre damage evolution law is proposed for the problem of fatigue life estimate under low number of cycles. For this, the denominator of damage, considered constant for Lemaitre, was replaced by a function dependent on the stress triaxiality. The new function has a nonlinear and thermodynamically consistent behavior. In addition, the evolution law of the backstress tensor is adopted as proposed by Desmorat, where there is no saturation of the limit value. The formulation is implemented in an academic tool for analysis at one Gauss point, through an implicit integration strategy of the flow equations. The Newton-Raphson method is used to solve a system of nonlinear equations, with two tensor and two scalar equations. Thus, in order to demonstrate the robustness of the model, experimental data from the literature for SAE 1045 and S460N steels are adopted. Proportional and nonproportional axial, torsional and multiaxial loading paths are simulated. Finally, the results have shown that the modification formulation is a good strategy to control the damage evolution in predicting fatigue life. In this sense, the calculated lives by the new proposal are within a scatter band of factor three, both under normal or torsional uniaxial loading conditions, as well as proportional or nonproportional multiaxial conditions.

On the use of acoustic emission to identify the dominant stress/strain component in carbon/epoxy composite materials

Acoustic Emission (AE) is casually employed for monitoring the mechanical behaviour of composite media as the amount of damage and the different fracture modes can be well characterised through the evolution of the AE characteristics. However, the sensitivity of the technique allows for more than just classification of the existing damage modes in composite materials. In the present paper, the limits of AE are further pushed as it is used to characterise the stress/strain field developing in composite laminates even before damage mechanisms become evident. In addition, the change of the strain field due to damage evolution during quasi-static and fatigue experiments, as monitored by real-time Digital Image Correlation (DIC), is depicted on the shift of the AE parameters. This is of great importance in cases that detrimental shear stresses are generated in the material, leading to important interlaminar delaminations and mechanical deterioration. AE can be used in this direction to predict the upcoming damage modes and to take the necessary measures to avoid final catastrophic failure by applying intermediate repair approaches. The examined material in this study is angle-ply Carbon Fibre Reinforced Polymer (CFRP) composite laminates consisting of different off-axis plies, in which different multiaxial conditions are generated due to the inherent anisotropy of composite materials. It is demonstrated that AE can identify the dominant stress/strain component rather than just the occurring damage mode even at early loading stages, before severe fracture influences the mechanical capacity of the material.v© 2020 The Authors. Published by Elsevier Ltd.

Prediction of uniaxial creep rupture and crack growth using a micro/macro constraint criteria model for various steels

Stress/strain measured data which have inherent scatter are used to develop predictive models in creep failure assessment under uniaxial and multiaxial conditions. Models developed for this purpose also need to address the multiaxial stress state eff

Creep rupture time prediction methods of 2.25Cr-1Mo steel under multiaxial stress gradient condition

Creep rupture time prediction methods of 2.25Cr-1Mo steel under multiaxial stress gradient condition

Multiscale-constraint based model to predict uniaxial/multiaxial creep damage and crack growth in 316-H steels

A new failure ductility/multiscale constraint strain-based model to predict creep damage, rupture and crack growth under uniaxial and multiaxial conditions is developed for 316H Type stainless steels by linking globally uniform failure strains with a multiaxial constraint factor. The model identifies a geometric constraint and a time-dependent local constraint at the sub-grain level. Uniaxial and notched 316H steel as-received and pre-compressed data at various load levels and temperatures with substantial scatter were used to derive the appropriate constitutive equations by using the proposed empirical/mechanistic approach. Constrained hydrostatic development of creep damage at the sub-grain level is assumed to directly relate to the uniform lower-bound creep steady state region of damage development measured at the global level. Uniaxial and notched bar rupture at long terms is predicted based on the initial short-term creep or a representative tensile strength and a multiaxial constraint factor. The model is consistent with the well-known NSW remaining multiaxial ductility creep crack growth model which predicts crack growth bounds over the plane strain/stress states. This model, therefore, unifies the creep process response over the whole range of uniaxial, notched and crack growth processes which is extremely consequential to simple long term failure predictions of components at elevated temperatures.

A railway wheel evaluation under multiaxial loading conditions

Railway mechanical components are subject to thousands of fatigue cycles. Fatigue damage and life assessment is still an open issue. Under service multiaxial loading conditions several challenges can arise. In this study an evaluation of a railway wheel material is performed, i.e. the material properties and the working conditions are taking into account and evaluated. Different mechanical tests are carried out, namely fatigue tests under uniaxial (LCF+HCF) and biaxial (HCF) conditions, applied to several specimens made from the railway wheel. Multiaxial fatigue models were considered regarding the fatigue life estimation. Moreover, fatigue crack plane measurements were compared with estimations from several critical plane models. The applied models provided very satisfactory results, regarding the fatigue life estimation and the initial crack initiation plane under the multiaxial loadings conditions.

A three-dimensional elastoplastic analysis of mixed-mode KI/KII around the crack front

Engineering problems that involve fatigue crack growth and fracture frequently can be studied by taking into account only mode-I features. However, many important problems that involve combined mode I and II loadings cannot be properly analyzed by a pure mode-I approach, which in particular may not be sufficient to estimate fracture toughness for practical purposes in such cases. Such mixed-mode problems involve crack orientation and/or load conditions that lead to combined local Stress Intensity Factors (SIFs) KI/KII around the crack front. Using multiaxial crack tip condition characterized by the crack inclination angle βin a mixed-mode KI/KII modified single edge tension SE(T) specimen, such mixed-mode effects on plastic zone shapes, volumes and plastic work UPL are taken into account to evaluate problems that involve fatigue and fracture.

Multiaxial ultra low cycle fatigue in welded high strength steel structural components

Extreme events often subject regions of structural steel components to large inelastic strains. In conditions such as earthquakes, exceptional winds gusts or tides the loading scenario is cyclical, variable amplitude and frequently multiaxial in nature, and failure of a component can often be atributed to a phenomenon known as ultra low cycle fatigue (ULCF). Failure in this regime is reached typically within ten to twenty cycles as a consequence of the sizable amplitudes to which the material is strained. This paper focuses on a methodology to assess welded high strength steel component resistance to ULCF using a local approach. More than sixty tube to plate joints experiments on welded high strength steel (S770QL) are presented. These components were submitted to high cyclic bending, pure torsional and combined proportional bending and torsional loadings and variable amplitude loading. Weld profile and strain measurements (up to 10% amplitude) at the weld toe were performed using digital image correlation (DIC). These original results using DIC measurements suggest that using a local equivalent strain metric at the weld toe provides a consistent resistance model in strain-life terms. Mesh requirements in line with local approaches to fatigue are proposed for finite element simulation assessment of ULCF strength in multiaxial conditions for high strength steel.

Study of the Structure Formation during Compression for Selecting Multiaxial Deformation Conditions for an Mg–Ca Alloy

The structure homogeneity of the Mg–0.8% Ca alloy is shown to increase with temperature during uniaxial compression. Plastic deformation localizes in narrow and wide deformation bands at 250–350°C. A small number of regions with recrystallized grains is observed only after deformation at 400°C. A relatively homogeneous recrystallized structure with an average grain size of about 20 μm forms after uniaxial compression at t = 450°C. Multiaxial deformation at decreasing temperature in the range 450–250°C significantly refines the initial structure of the Mg–0.8% Ca alloy to an average grain size of 2.1 μm. This structure leads to a significant hardening, namely, an increase in the yield strength to 193 MPa and the tensile strength to 308 MPa. The relative elongation after multiaxial deformation increases by more than two times.

Fatigue Design Evaluation of Railway Bogie with Full-Scale Fatigue Test

The bogie frame of a railway is an important structural member for the support of vehicle loading. In general, more than 25 years’ durability is necessary. Much study has been carried out in experimental and theoretical domains on the prediction of the structural integrity of the bogie frame. The objective of this paper is to estimate the structural integrity of the bogie frame of an electric railcar. Strength analysis has been performed by finite element analysis. From this analysis, stress concentration areas were investigated. To evaluate the loading conditions, dynamic stress was measured by strain gauge. It has been found that the stress and strain due to the applied loads were multiaxial conditions according to the location of the strain gauge. Fatigue strength evaluations of the bogie frame were performed to investigate the effect of a multiaxial load through the employment of a critical plane approach.

Numerical implementation of a multiaxial cyclic plasticity model for the Local Strain method in low cycle fatigue

Very often computations on structural elements or machine components subjected to variable loading require the use of an advanced finite element model. This paper reports the numerical implementation of a model for multiaxial cyclic elasto-plastic behaviour, developed to extend the tools of the Local Strain method to fatigue under multiaxial conditions. A basic computer code for axial–torsional loads was developed with the commercial software MATLAB and a more sophisticated one, for general multiaxial loads, was developed as a UMAT subroutine in ABAQUS. Stress integration was introduced in the two usual forms: implicitly and explicitly. A comparison of the results obtained with the implicit and explicit formulations revealed that, under certain loading conditions, the outcome of the process depends very much on the particular integration scheme used.

Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics*

The mechanical behavior of monolithic cementitious materials is known to be significantly affected by their granular nature. This paper describes an approach to incorporate the effects of granularity for cementitious material based upon the granular micromechanics paradigm and thermomechanics. As a result, macro-scale constitutive equations that utilize grain-scale force–displacement relationships have been derived. In this derivation, the connections between grain-scale free energy and dissipation and the macro-scale behavior are established based upon the thermomechanics framework. Expression for Cauchy stress tensor is obtained in terms of the free energy of grain-pair interactions. In addition, the free energy and dissipation potential of grain-pair interactions are used to find a grain-scale Clausius–Duhem type inequality. Thus, inter-granular constitutive equations are obtained in the usual manner with the exception that these are based upon simple physically motivated free energy and dissipation functions formulated in terms of grain-pair interactions. The derived model is used to simulate a wide variety of experimental tests that have been reported in the literature to evaluate material response under multi-axial conditions. The results are analyzed with the aim to reveal the connections between grain-scale mechanisms and the macro-scale behavior.

Numerical implementation of a multiaxial cyclic plasticity model for the Local Strain Method in low cycle fatigue

Very often computations on structural elements or machine components subjected to variable loading require using an advanced finite element model. This paper reports the numerical implementation of a model for multiaxial cyclic elasticplastic behaviour developed to extend the tools of the local deformation method under fatigue to multiaxial conditions. A basic computer code for axialtorsional loads was developed with the commercial software Matlab and a more sophisticated code based on the finite element model for general multiaxial loads was developed as a UMAT subroutine in Abaqus. Stress integration was introduced in the two usual forms: implicitly and explicitly. A comparison of the results obtained with the implicit and explicit formulations revealed that, under certain loading conditions, the outcome of the process depends on the particular integration scheme used.

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

ABSTRACTThe local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.

Numerical Simulation of Stress Intensity Factor under Multiaxial Loading

Based on the theory of fracture mechanics and finite element method, this paper presents a numerical calculation of typical experimental models, with emphasis on calculation of the stress intensity factor of I-type crack. A two-dimensional finite element analysis of a plate sample including an initial crack was carried out to study the propagation of a fatigue crack under multiaxial loadings. The effects of crack length and the multiaxial condition on the stress intensity factor were especially investigated. Our present approach provides an effective method for edge crack fracture criterion under complex loading calculation.

A damage based model for crack initiation in unidirectional composites under multiaxial cyclic loading

Abstract In the present work a criterion for the non-fibre (i.e. matrix or fibre–matrix interface) – controlled fatigue behaviour of composite unidirectional laminae subjected to multiaxial loading is proposed. The criterion is based on experimental observations of the damage modes occurring at the microscopic scale leading to the fatigue failure of a lamina. In particular two parameters have been identified as representative of the driving forces for the damage initiation, and they have to be used for design purposes depending on the local multiaxial condition. These parameters, i.e. the local maximum principal stress and local hydrostatic stress, are calculated from the local stresses in the matrix, obtained from Finite Element analyses of a fibre/matrix unit cell subjected to periodic boundary conditions. The application of the proposed criterion to fatigue data taken from the literature shows that only two scatter bands can be used to completely describe the fatigue response of unidirectional laminae under generic multiaxial stress states.

The cyclic and evolutionary response to approach the attraction loops under stress controlled isothermal conditions for a multi-mechanism based multi-axial SMA model

The main focus in the present work has been on studying the evolutionary responses of Shape Memory Alloy (SMA) materials under isothermal, cyclic loading conditions. To this end, predictions of a recently-developed SMA material model by the authors is used here to carry out the qualitative comparisons to some of the available experimental results in the literature for SMA material responses under different uniaxial and multi-axial conditions of stress-control, both in the pseudoelastic and the pseudoplastic regimes. In the formulation of this model, the significant roles played by the internal state variables, underlying the inelastic mechanisms in the model to regulate the material’s evolutionary response under extended cycles, are emphasized. The results presented have led to a number of important conclusions. First, the evolutionary character for pseudoelasticity is markedly different from that occurring in the pseudoplastic regime. Second, the virgin material response under minor loop cycles is dramatically different from its pre-cycled counterpart for which a prior major loop was established. Third, the careful selection of the loading-control variable such as magnitudes of the mean stress and stress amplitude plays a major role in dictating the amount of strain and detailed shapes of the saturated stress–strain loop achieved, as well as the number of cycles required to reach the saturation. Lastly, multi-axial load cycling under conditions of combined tension/compression/shear leads to a faster approach to the saturated states compared to the uniaxial load condition.

G031063 SUS304鋼の高温多軸疲労き裂進展に対する位相差,及びスリット形状の影響([G031-06]材料力学部門,一般セッション : き裂疲労)

Effects of phase difference and slit geometry on high temperature fatigue crack growth of SUS 304 stainless steel were examined under multiaxial conditions. Fatigue crack growth tests were conducted by using DC electrical potential drop method. "Tensile type" crack, which propagates along the direction, φ, perpendicular to the maximum principal stress, σ_1 and "Shear type" crack, which propagates along the direction of maximum shear stress, γ_<max> were observed under these conditions. The appearance of crack growth type was affected by both slit geometry and phase difference of loading waveform, as well as multiaxial condition, Δγ/Δσ. In case of the slit with low stress concentration, "Shear type" crack growth tends to be appeared. The experimental results were discussed with the results of elastic-creeping FE analyses for under combined loading conditions. The characteristics of both type of fatigue crack were discussed.