Concept Of Equivalent Stress Research Articles

Equivalent stress concept to account for the effect of local cyclic stress ratio on transverse cracking in tension–tension fatigue

Presented test results on transverse cracking in cross-ply laminates upon tension–tension cyclic loading show that the increase of crack density depends not only on the maximum transverse stress in the cycle but also on the local cyclic stress ratio RTloc in the analyzed layer. To include the effect of the RTloc in the model with statistical failure stress distribution for crack initiation (based on Weibull distribution) adapted for fatigue, an equivalent stress is introduced in a similar manner as the equivalent strain energy release rate has been used for delamination crack propagation. The equivalent stress in the layer is defined as a power function of the maximum stress and the stress ratio in the layer. It was found, testing laminates with two different fiber contents that higher the local stress ratio in 90-layer, higher the transverse cracking resistance. Transverse crack density simulation using the developed equivalent stress model has been validated against test results.

Thermo-mechanical volume change behavior of municipal solid waste: experimental study and constitutive model

This paper investigates the thermo-mechanical volume change behavior of municipal solid waste (MSW) by conducting drained heating–cooling tests at constant stresses and isothermal consolidation tests using a temperature-controlled triaxial apparatus. The experimental results show that the compression and swelling indexes of MSW specimen were temperature independent, and the heating-induced volumetric contraction was partially reversible upon cooling. Different from conventional soils, the thermally induced reversible and irreversible volumetric strains of MSW were much larger and stress level dependent. Apart from the experimental study, an isotropic thermo-elastoplastic constitutive model was developed in the framework of existing modified Cam-clay model, which allows the prediction of thermally induced volume changes of MSW. An important feature in this model was the derivation of thermally induced plastic volumetric strain based on the concept of equivalent stress. The capability of the proposed model was validated against the experimental results and showed good predictions. This paper serves as the first attempt to study the thermo-mechanical volume change behavior of MSW, and has provided additional data for the serviceability evaluation of existing pipes as well as settlement and capacity estimation of MSW landfills at elevated temperatures.

Regularization of free discontinuity problem and its application in the simulation of brittle fracture of concrete

As a free discontnuity problem, the predicton of the path that a crack chooses while it propagates through a britle material has been a long standing problem in fracture mechanics. To circumvent the mathematcal difcultes in the modeling of fracture behaviors, this paper takes advantage of the regularizaton approach to approximate the Munford-Shah functonal with Γ-convergence. The governing equatons of physical felds are constructed based on the concept of energy minimizaton. This method is capable of capturing the crack initaton and propagaton without a specifc tracking algorithm. Additonally, a pure elastc phase can be considered by introducing an energy threshold. By the use of the concept of equivalent stress, a stress-based fracture governing criterion was established. The numerical implementaton is based on a standard fnite element discretzaton and on the staggered algorithmic. Two classic concrete fracturing tests were investgated to demonstrate the performance of the model by comparing the numerical results with experimental results.

Multiaxial fatigue damage evaluation: A new method based on modal velocities

The present work aims at finding an approach to calculate fatigue damage from three-dimensional vibration measurements, with a key objective to define a reliable measurement quantity to predict local stresses. Existing theoretical concepts highlight an exploitable relation to modal velocity. A hysteresis counting based on velocity measurements as well as damage accumulation using S–N curves is proposed. While existing methods consider only uniaxial shaker test setups, there is also a need for fatigue calculation under a three-dimensional shaker setup. This paper also derives a method for fatigue calculation for structures under three-dimensional excitation using the equivalent stress concept. The proposals are also validated using a real mechanical structure and the results indicate better applicability than existing methods.

Comparison of Strength Criteria Based on the Measurements on Concrete

To evaluate an arbitrary multiaxial stress state, the concept of the equivalent stress can be used. Because of its simplicity and clarity, this concept is now widely used in the component design. Many strength criteria based on the equivalent stress concept have been formulated during the last two centuries. Currently, a large number of strength criteria are available. The choice of an appropriate criterion for a particular material is the main challenge in applications. The alternative is the formulation of generalized criteria that contain classical strength hypotheses and are suitable for different materials. The generalized criteria of specific studies are selected in this work to describe experimental data for concrete. The generalized strength criteria contain several material parameters. The application of these criteria requires experimental results under multiaxial stress states in addition to tension, compression, and torsion test data. As an example, experimental data for concrete under plane stress loading are the focus of this study. These data are approximated with the help of the chosen criteria. The recommendations for the application of the generalized criteria are provided.

Uniaxial equivalent of stress and stress intensity factor in Mode I crack opening for fatigued metals subjected to multi parametric external loading

The principles of physical mesomechanics and synergetics, provides for a measure of energy involved in the ability of a material to resist deformation and fatigue cracking used for introducing a concept of equivalent stress and stress intensity factor in Mode I crack opening of fatigued metals. Acquired under the standard test conditions, the curves of unidirectional tension and those of fatigue duration and of crack-growth kinetics show themselves applicable as universal master-diagrams descriptive of the material behavior though under multiparametric loading. Specimen patterns of fracture, revealed by the test pieces of metallic alloys given to asymmetrical biaxial loading or multiparametric loading, passed careful research. In the biaxial case, this research facilitated finding of the view of the correction function for the level of equivalent stress and, in the multi-axial case, employing of the above subject ideas to ascertain the very level of equivalent stress.

A new yield and failure theory for composite materials under static and dynamic loading

To facilitate and accelerate the process of introducing, evaluating and adopting new material systems, it is important to develop/establish comprehensive and effective procedures of characterization, modeling and failure prediction of composite structures based on the properties of the constituent materials, e.g., fibers, matrix, and the single ply or lamina. A new yield/failure theory is proposed for predicting lamina yielding and failure under multi-axial states of stress including strain rate effects. It is based on the equivalent stress concept derived from energy principles and is expressed in terms of a single criterion. It is presented in the form of master yield and failure envelopes incorporating strain rate effects. The theory can be further adapted and extended to the prediction of in situ first ply yielding and failure (FPY and FPF) and progressive damage of multi-directional laminates under static and dynamic loadings. The significance of this theory is that it allows for rapid screening of new composite materials without extensive testing and offers easily implemented design tools.

Generalized Strength Criteria as Functions of the Stress Angle

AbstractThe equivalent stress concept allows the comparison of arbitrary multiaxial stress states with a uniaxial one. Based on this concept several limit surfaces were formulated. The trend in the...

Ferromagnetic resonance in thin films submitted to multiaxial stress state: application of the uniaxial equivalent stress concept and experimental validation

In this paper a unique expression of the anisotropy field induced by any multiaxial stress state in a magnetic thin film and probed by ferromagnetic resonance is derived. This analytical development has been made using the uniaxial equivalent stress concept, for which correspondances between definitions given by different authors in the literature is found. The proposed model for the anisotropy field has been applied to thin films (25 nm) stressed both by piezoelectric actuation (non-equi-biaxial) or by bending tests (uniaxial) and measured with a broadband ferromagnetic resonance technique. The overall exprimental data can be easily plotted on a unique graph from which the magnetostriction coefficient has been estimated.

Effect of temperature on the time-dependent behavior of geomaterials

In many geotechnical engineering applications, such as nuclear waste disposal and geothermal extraction and storage, it is necessary to consider the long-term mechanical properties. The effect of temperature could have a complicated influence on the creep damage behavior of soft rock. As a consequence, it is meaningful, both in theory and in practice, to establish a constitutive model that can describe the creep damage behavior. Within the framework of continuum mechanics, a thermo-visco-elastoplastic model is proposed on the basis of a sub-loading Cam-clay model and the concept of equivalent stress. Triaxial creep tests under different confining pressures for Tage stone were conducted to validate the proposed model. The experimental results show that an optimum temperature exists for a certain stress state, and this temperature significantly slows down the creep damage rate. In addition, both the retarding and accelerating effects on creep rupture due to limited warming are observed for the same material, and this phenomenon can be predicted well by the proposed model. Finally, a parametric analysis is performed, and the influence of the material parameter on creep regularity is discussed in detail.

Fitting of the strength hypotheses

The equivalent stress approach allows the comparison of arbitrary multiaxial stress states with a uniaxial one. Based on the concept of the equivalent stress, several strength hypotheses (limit surfaces) were formulated. These hypotheses take into account not only existing information from the tests. They can also describe a experiences and different expectations concerning the material behavior mathematically. Due to the simplicity and clarity, the equivalent stress concept is widely used. Collected experimental data, applications, and know-how make this approach an extremely powerful tool for engineering design. The method can also be easily applied in the case of new materials. As an example, polymethacrylimide (PMI) hard foam ROHACELL® 110IG, from manufacturer Evonik Rohm GmbH (Darmstadt), will be in the focus of this study. Modern strength hypotheses are functions of several parameters. The application of these hypotheses requires in addition to tension, compression, and torsion test data further experimental results. Such data are often not reliable or widely scattered. Hence, the adjustment of the parameters of the chosen hypothesis is not unique. Some extrapolations with respect to the hydrostatic stress states can lead to unacceptable results and, therefore, the parameters must be restricted. In this work, several restrictions based on the principles of conservative material description are introduced. They adjust a shape of the limit surface in the principal stress space. These restrictions are geometrically justified. The influence of various restrictions on the limit surface is analyzed. The effectiveness is tested with the help of own measured data. Reliable material descriptions for hard foams will be suggested.

Equivalent Stress Model for Magnetic Hysteresis Losses Under Biaxial Loading

The concept of equivalent stress for hysteretic behavior is discussed. Magnetic measurements are first performed on iron-silicon thin sheets subjected to biaxial stress. Both anhysteretic and dissipative magnetic responses are recorded. An anhysteretic equivalent stress for the magnetic susceptibility is first applied. A configuration effect allows building an equivalent stress for the coercive field. The combination of the two formulations leads to a prediction of losses in the stress plane.

Giant Magnetostrictive Materials for Field Weakening: A Modeling Approach

In this paper, a proposal for a field weakening method for a permanent-magnet synchronous motor is evaluated. The method consists in inserting giant magnetostrictive elements between permanent magnets. The magnetic permeability of these magnetostrictive parts is modified when the speed increases. The field leakages around the permanent magnets are consequently increased, thus reducing the electromotive forces in the armature windings. An original modeling approach, based on the concept of equivalent stress, is proposed in order to evaluate this field weakening solution.

Saturated and unsaturated behaviour modelling of Meuse–Haute/Marne argillite

Poromechanical behaviour modelling of the Callovo–Oxfordian argillite under saturated and partially saturated conditions is proposed using the equivalent stress concept. In comparison with the previous works on this rock, the particular form of the yield criterion and the plastic flow potential proposed here help to better describe the rock behaviour in tension–stress paths. The evolution of the poroelastic parameters due to the induced cracks is also considered in a simple way. Due to its physical nature, different from classical soils, the partially saturated behaviour of this rock could not be correctly described by any of the pre-existing theories usually used for the partially saturated porous media (soils). Based upon experimental results on this rock and developing some ideas proposed by other authors, an extension of the saturated elastic–plastic model in unsaturated field is proposed. The key hypothesis of this extension is the evolution of the Biot’s coefficient as a function of the suction, justified by laboratory results and micromechanical analyses. The predictions of the model in saturated and partially saturated conditions are compared with laboratory results and a good general agreement is found.

Time to Creep Failure of Thin-Walled Cylindrical Pipes under Torsion

The time to creep failure is calculated for rectilinear thin-wall pipes subjected to pure torsion, torsion with uniaxial tension, and torsion with internal pressure. The problem is solved using the concept of equivalent stress. The equivalent stresses are found from the generalized mixed failure criterion whose form depends on the signs of the principal stresses. The criterion relates the maximum normal stress and the intensity of shear stress if the signs coincide, and the maximal shear stress and the octahedral shear stress if the signs are opposite. A technique for determining the material constants is developed. The calculated and experimental data are compared and found to be in satisfactory agreement

Nonlinear constitutive behavior of soft and hard PZT: experiments and modeling

This work characterizes and models the nonlinear inelastic behavior of lead zirconate–titanate (PZT) ceramics. A detailed investigation of the hysteresis loop of the stress–strain curve shows that the process of ferroelastic non-180° polarization switching and of switching saturation are, respectively, a smooth softening process and a gradual hardening process. The inflection point in the curve is found to be a boundary point that distinguishes the transition from a softening process to a hardening one. Based on underlying physical mechanisms, this nonlinear behavior is simulated by a mechanical model, consisting of several parallel-arranged Maxwell chains with each chain taking a main role in a different, successive stage of the switching process. Each chain includes a nonlinear spring and a frictional slider. The generalized displacement of the slider, indicating an internal variable, is introduced to describe the local process of the cooperative switching of the corresponding grain group. The hardening and softening processes are controlled by variations of stiffness of the nonlinear springs. Furthermore, the observed similarities between the hysteresis loop of the stress–strain curve and that of stress–electric displacement curve are used to develop an equivalent stress concept and to formulate constitutive laws for PZT ceramics. Comparisons between the experimental hysteresis loops and those calculated by the proposed model show satisfactory agreement for both hard PZT and C5800 and soft C5500.

Effect of Three-Dimensional Near Surface Defects on Rolling and Sliding Contact Fatigue

The effect of three-dimensional defects such as voids and inclusions on the sliding contact subsurface stress distribution and fatigue limit is investigated. Three-dimensional finite-infinite boundary elements are utilized to model the body by discretizing its surface and the interface between the solid and the defect. The multidomain boundary element formulation is employed to accurately model the effect of the inclusion on the stress distribution. It is shown that the void has a greater near field effect on the stress distribution while the effect of a stiff inclusion applies over a larger distance. The critical stress points during a load passage are predicted based on a search of the maximum distortional strain energy. The stresses at the critical points are used for the fatigue limit pressure estimation by incorporating the equivalent stress concept with the Haigh diagram. The model predicts that a near surface spherical void of given size and depth reduces the maximum allowable fatigue limit design pressure by 75 percent while a stiff inclusion of the same size, shape, and location reduces it by 25 percent.

A prediction of equibiaxial stress-strain curves of sheet metals

Many studies show correlation between the experimental stress-strain curves of sheet metals as determined from different deformation modes, such as plane strain tension and balanced biaxial tension, predicted from a uniaxial tensile test by the equivalent concept, through different anisotropic yield criteria. In this paper, an attempt is made to predict the balanced biaxial stress-strain curves of aluminium and copper sheets from their uniaxial tension data, without using the concept of equivalent stress or strain. The model takes into account a sheet's initial preferred orientations, external imposed constraints, and crystal rotations along the strain path that the sheet metal will follow.

Fatigue Life Prediction Considering Constraint of Notches.

A fatigue life prediction procedure was discussed from the viewpoint of the constraint effect of notches. In this report, fatigue crack initiation lives were used to avoid the fatigue crack propagation process and the prediction procedure was examined experimentally. It was fouud that fatigue crack initiation lives depend on the local strain amplitude at the notch root, and the constraint effect of notches to fatigue crack initiation lives may be considered as the multiaxial effect at the notch root and might be evaluated through the equivalent stress concept as used in the multiaxial fatigue problem. The experimental results showed good agreement with the proposed fatigue life prediction procedure.

Lateral pressure in a stiff clay : Schulz, H; Khera, R P Proc Symposium on Geotechnical Aspects of Stiff and Hard Clay, Seattle, 9 April 1986, P44–59. Publ New York: ASCE, 1986

A series of consolidated undrained and drained triaxial tests and oedometer tests were performed on horizontal and vertical specimens taken from an overconsolidated cretaceous clay. An equivalent stress was defined and used for normalizing the test data. A regression analysis of the data points indicated that the relationship between undrained strength and plasticity index, developed by A. W. Skemtpon, was applicable to this soil if the concept of equivalent stress was used. From critical state soil mechanics, a method for determining earth pressure at-rest was developed. A comparison between the measured values of the lateral pressure using pressuremeter and the predicted values showed a reasonable agreement.