Resulting Stress State Research Articles

Strain rate and orientation dependencies of the strength of single crystalline copper under compression

Molecular dynamics (MD) simulations are used to model the compression under uniaxial strain of copper single crystals of different orientations at various temperatures and strain rates. Uniaxial strain is used because of the close resemblance of the resulting stress state with the one behind a shock front, while allowing a control of parameters such as strain rate and temperature to better understand the behavior under complex dynamic shock conditions. Our simulations show that for most orientations, the yield strength of the sample is increased with increasing strain rate. This yield strength is also dependent on the orientation of the sample, but less dependent on temperature. We find three regimes for the atomistic behavior around the yield: homogeneous dislocation nucleation, appearance of disordered atoms followed by dislocation nucleation, and amorphization. Finally, we show that a criterion solely based on a critical resolved shear and normal stress is insufficient at these strain rates to determine slip on a system.

Fabric dilatancy and the plasticity modeling of granular media

SUMMARYA novel conceptual model of the mechanics of sands is developed within an elastic–plastic framework. Central to this model is the realization that volume changes in anisotropic granular materials occur as a result of two fundamentally different mechanisms. The first is purely kinematic, dilative, and is the result of the changes in anisotropic fabric. There is also a second volume change in granular media that occurs as a direct response to changes in stress as in a standard elastic/plastic continuum. The inclusion of the two sources of volume change results in three important datum states. When subjected to isotropic strains, the resulting stress state in granular materials is not isotropic but lies upon the kinematic normal consolidation line. There exists a state at which the fabric‐induced volumetric strain rate becomes equal to the stress‐induced volumetric strain rate making the total plastic volumetric strain rate equal to zero. Granular response changes from contractive to dilative at this phase transformation line. The third datum state is the one in which the stress‐induced volumetric strain rate is zero. The sand, however, continues to dilate at this state with the difference between stress and dilation ratio a constant as predicted by Taylor's stress–dilatancy rule. These predictions are shown in accordance with experimental data from a series of drained tests and undrained on Ottawa sand. Copyright © 2011 John Wiley & Sons, Ltd.

Stress analysis for a cavity flow of a memory fluid

The paper deals with the plane creeping flow of a viscoelastic liquid within an idealized rotor–stator system consisting of a rotating cylindrical drum and a fixed internal plate. The rheological properties of the liquid are modelled by a single-integral constitutive equation which considers a memory but disregards shear-thinning features. It is pointed out that the flow kinematics of such a memory fluid deviates only marginally from the Newtonian kinematics whereas the stress field is much more complicated. Therefore, the Newtonian velocity field is applied which can be represented in a closed analytical form using elementary complex-valued functions. The formulation allows computing the strain history and the resulting stress state with little numerical effort. A careful asymptotic analysis close to the corners yields details of the singular stress behaviour which differs markedly from the Newtonian characteristic. Finally, a second-order approximation being valid under certain restrictions leads to explicit analytical expressions also concerning the viscoelastic stress components. Altogether, a well-founded insight as regards the complex stress distribution and the effect of Deborah number is attained.

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

A Test Fixture for Fully Reversed Axial Fatigue Characterization of Composites

Abstract Fatigue of fiber-reinforced polymer matrix composites has been studied exhaustedly over the years. However, most fully reversed fatigue testing has concentrated on flexural fatigue. The resulting stress state through the laminate thickness is non-uniform and as such may give rise to unconservative life estimates. Fully reversed (R=−1) axial testing has not been heavily reported due to the difficulties associated with precluding local or global buckling of the axial specimen. The few reported fully reversed axial tests utilize either cylindrical specimens or fixturing that is very large, expensive to fabricate, and difficult to handle. Herein we report on a simple side support fixture that allows the use of standard ASTM tensile test specimens (D3039 or D638, depending on test material), which are readily prepared. The fixture allows fully reversed axial fatigue testing as well as static baseline compression and residual compression strength characterization. Also presented herein are tension-tension (R=0.1) and fully reversed tension-compression (R=−1) S-N diagrams for an E-glass/epoxy composite.

An anisotropic fibre-network model for mechano-sorptive creep in paper

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.

Mechano-sorptive creep under compressive loading – A micromechanical model

The creep of paper is accelerated by moisture cycling, an effect known as mechano-sorptive creep. It has also been observed that the mechano-sorptive effects are larger in compression than in tension. In this paper a simplified network model for mechano-sorptive creep is presented. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre–fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys constitutive laws that are non-linear in stress. Geometrical fibre effects are included in the model in order to capture experimental observations of the differences between paper loaded in tension and compression. Theoretical predictions based on the developed model are compared to experimental results for paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model, i.e. the creep is accelerated by the moisture cycling and the mechano-sorptive effects are larger in compression than in tension.

Response of Kidney Tissue to Dynamical Loading

AbstractIn shock‐wave lithotripsy – a medical procedure to fragment kidney stones – the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries of the surrounding kidney tissue arise, is still under investigation. Here we contribute to the solution of this problem with large scale numerical simulations of a human kidney under shock‐wave loading.For this purpose we developed a complex constitutive model of the bio‐mechanical kidney system. Assuming a multiplicative decomposition of the deformation gradient and adopting an internal variable formulation for the inelastic deformation the model is able to handle large deformations, time‐effects, rate‐sensitivity and material damage.By finite element simulations we study the shock‐wave propagation into the kidney tissue and analyze the resulting stress states. Unknown material parameters are adapted and special attention is paid on the bubble expansion within the soft tissue. The numerical simulations predict localized damage in the human kidney within the focal region of the shock waves. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The modelling of residual stresses due to surface peening using eigenstrain distributions

The beneficial effect of surface peening (including shot peening, laser shock peening, low plasticity burnishing, etc.) on fatigue resistance of structural alloys is well documented and widely used in industry to improve component life. It is perhaps the most widely used technique that relies on the introduction of residual stresses into the component by direct mechanical means. The resulting stress states are usually evaluated experimentally by X-ray diffraction or other stress measurement techniques. In order for shot peening operations to be effective and reliable, the process of introducing residual stresses and strains into peened components must not only be controlled but also be predictable and quantifiable. The present paper establishes a framework for predictive modelling of the residual stress states due to surface peening. Firstly, uniform (within planes parallel to the surface) plastic deformation of the surface layer taking place during shot peening of a thin plate is simulated using the concept of eigenstrain. As a further demonstration of the capabilities of the proposed approach, flexible plate theory is applied to the analysis of stresses and deformations arising due to local peening within a circular area. The results are of considerable use and significance for the analysis of shot peening and peen forming operations.

A Model for Kidney Tissue Damage under High Speed Loading

AbstractIn a medical procedure to comminute kidney stones the patient is subjected to hypersonic waves focused at the stone. Unfortunately such shock waves also damage the surrounding kidney tissue. We present here a model for the mechanical response of the soft tissue to such a high speed loading regime.The material model combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. The theory is based on a multiplicative decomposition of the deformation gradient and on an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small‐strain to the finite deformation range. In that way the time‐discretized version of the porous‐viscoplastic constitutive updates is described in a fully variational manner.By numerical experiments we study the shock‐wave propagation into the tissue and analyze the resulting stress states. A first finite element simulation shows localized damage in the human kidney. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermoelastic Stresses in an Axisymmetric Thick-Walled Tube Under an Arbitrary Internal Transient

A closed-form axisymmetric solution was derived for the transient thermal-stress fields developed in thick-walled tubes subjected to an arbitrary thermal loading on the internal surface with convection to the surrounding external environment. Generalization of the temperature excitation was achieved by using a versatile polynomial composed of integral-and half-order terms. In order to avoid the difficult and potentially error prone evaluation of functions with complex arguments, Laplace transformation and a ten-term Gaver-Stehfest inversion formula were used to solve the resulting Volterra integral equation. The ensuing series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress-states. Excellent agreement was seen between the derived temperature and stress relationships, existing series solutions, and a finite-element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature. The use of a smoothed polynomial in the derived relationships allows the incorporation of empirical data not easily represented by standard functions. This in turn permits an easy analysis of the significance of the exponential boundary condition and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Moreover, the resulting relationships are easily programmed and can be used to verify and calibrate numerical calculations.

異方性を考慮した孔変形方式の応力解放地圧測定法の開発および等方解析の誤差

Overcoring rock stress measurement method has been used in most of projects of constructing large rock caverns for hydro-power plants and oil storage in Japan. This is because the principle of the method is clear and reliable measurement devices have been developed. Overcoring stress measurement method is applicable to both isotropic and anisotropic rocks, but only methods assuming isotropy have been actually available in engineering. Rock is sometimes very anisotropic and the importance of considering anisotropy in rock stress measurement has been pointed out by several authors. One of the major reasons for the fact that there has been no practical method taking into account the anisotropy is that it has been very difficult to determine anisotropy of the rock at the location of the overcoring.In this paper, adopting a new method for determining orthotropic anisotropy by pressurizing a hollow cylinder, a practically applicable rock stress measurement method is developed. Then an example of applying the method to a field data is shown. Further, the error in the resultant stress state when isotropy is assumed for anisotropic rock is discussed through many simulations.

Influence of flow stress and specimen geometry on the fracture morphology of Nickel 270

The effects of flow stress and specimen geometry on the fracture morphology of Nickel 270 were studied experimentally and computationally. Tensile tests were performed on cold worked and annealed specimens with two gauge geometries. Fractographic observations revealed that all specimens failed by microvoid coalescence and shear. The relative proportions of the two failure modes were a function of stress - strain response. Microvoid density and aspect ratio were influenced by changes in microstructure and specimen geometry. Computational simulations were performed for both gauge geometries for both the cold worked and annealed specimens in order to determine the stress states that developed in these specimens during loading. It was found that the changes in fracture morphology observed in these specimens are directly attributable to the resulting stress state history in a given specimen. Differences in ductility before failure initiation are consistent with changes in fracture morphology and stress state history.

Scaled boundary finite‐element analysis of a non‐homogeneous elastic half‐space

AbstractAs a result of stresses experienced during and after the deposition phase, a soil strata of uniform material generally exhibits an increase in elastic stiffness with depth. The immediate settlement of foundations on deep soil deposits and the resultant stress state within the soil mass may be most accurately calculated if this increase in stiffness with depth is taken into account. This paper presents an axisymmetric formulation of the scaled boundary finite‐element method and incorporates non‐homogeneous elasticity into the method. The variation of Young's modulus (E) with depth (z) is assumed to take the form E=mEzα, where mE is a constant and αis the non‐homogeneity parameter. Results are presented and compared to analytical solutions for the settlement profiles of rigid and flexible circular footings on an elastic half‐space, under pure vertical load with αvarying between zero and one, and an example demonstrating the versatility and practicality of the method is also presented. Known analytical solutions are accurately represented and new insight regarding displacement fields in a non‐homogeneous elastic half‐space is gained. Copyright © 2003 John Wiley & Sons, Ltd.

A new criterion for mixed mode fracture initiation based on the crack tip plastic core region

In this work, we propose a new criterion for mixed mode I-II crack initiation angles based on the characteristics of the plastic core region surrounding the crack tip. The shape and size of the plastic core region are thoroughly analyzed under different loading conditions and a new formulation for the non-dimensional variable radius of the core region is presented for mixed mode (KI−KII) fracture. The proposed criterion states that the crack extends in the direction of the local or global minimum of the plastic core region boundary depending on the resultant stress state at the crack tip. The results show a well-defined correlation between the plastic core region characteristics and crack extension angles predicted by other criteria. The proposed criterion is formulated for various loading conditions and is compared with other available criteria against the limited available experimental data. It is shown that the proposed criterion provides a better agreement with the experimental data.

Thermoelastic Analysis of Thick-Walled Vessels Subjected to Transient Thermal Loading

A closed-form solution was derived for the transient thermal fields developed in thick-walled vessels subjected to a plausible exponential heating on the internal surface with convection to the surrounding external environment. The resulting series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress states. The derived expressions allow an easy analysis of the significance of the exponential terms and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Excellent agreement was seen between the derived temperature and stress relationships and a finite element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature.

Social stress of variable intensity: physiological and behavioral consequences

Stress effects in humans depend on stress type, intensity, and duration. Animal models of social stress serve as good ways to mimic stress experienced in humans. However, the available stress paradigms pay little attention to the relationship between the intensity and the type of social stressors. The aim of the present work is to study behavioral and endocrinological consequences of social stress by varying the intensity and type of agonistic social contacts. Subjects were exposed to the attacks of an experienced fighter resident rat once a day for 4 consecutive days. Mild versus strong effects were studied by varying the length of daily confrontations (30 min vs. 4 h). The type of social confrontations was varied by ceasing or maintaining sensory contacts among contestants between encounters. Endocrinological variables were measured on the 5th day. Anxiety was assessed by means of the elevated plus-maze. The stress state depended on the length of daily encounters: 30-min encounters did not, whereas 4-h encounters did result in weight loss and chronic elevation of plasma corticosterone. The type of contacts between subjects and dominants also affected the resulting stress state: adrenal hypertrophy was obtained only when contacts between contestants were maintained between encounters. Although the mildest stress procedure (30-min encounters on 4 consecutive days) did not affect endocrinological variables, it resulted in subtle behavioral modifications that changed the anxiety-related effects of additional acute stressors. Thus, anxiety-related behavioral changes resulting from repeated mild stressors may be hidden factors that can have long-term consequences on the development of anxiety-like behavioral deficits. Results outline the necessity of studying the effects of social stressors of different intensities and different types.

Thermomechanics of pack ice

A thermodynamic formulation for pack ice is presented that includes a means of relating stresses in floes to thermally induced strain rates. The formulation combines some basic thermodynamics as detailed in previous research. The mechanics component includes viscous creep and mechanically induced strain rates due to typical floes being too large to bend or twist in response to spatially varying strain rates. Moreover, the rheology quantifies the impact of existing cracks in the floe on the overall strain rate in the floe and the resulting stress state. A paradigm is proposed which specifies tensile fracturing and the resulting stress relief as proportional to the amount of existing cracks in the floe and some measure of the tensile strength of the ice. This allows the thermomechanical equations to be used for both first‐year and multiyear floes by differentiating the two by the extent of existing cracks. The thermomechanical equations are applied in an inverse fashion to solve for flaw structure for a first‐year floe as well as a multiyear floe. This is done by matching stresses predicted by the thermomechanical equations to observed stresses in the floes. The results indicate that the top two thirds of the ice in the first‐year floe was relatively free of cracks while the bottom third of the floe had cracks covering ∼50% of the ice. In the multiyear floe, cracks covered 70% to 90% of the ice in the top two‐thirds of the floe while the bottom third of the floe had cracks covering ∼30% of the ice.

Modelling plasticity in finite bodies containing stress concentrations by a distributed dislocation method

An efficient method for the analysis of limited plasticity at stress raising features such as notches and holes in finite bodies has been developed. A network of stationary dislocations is used to simulate the plasticity and simple constant displacement boundary elements form the borders of the geometries. The notch or hole itself is implicitly included in the formulation by using specialized kernels for these features in an infinite plane, thereby improving the numerical efficiency. The cyclic plastic behaviour of an edge-notch in an infinite plane and a finite rectangular plate are analysed under elastic-perfectly plastic, plane strain conditions. Examples of the resulting stress state after stress redistribution and plastic shakedown are displayed which aid in the reliable prediction of component life.

Coupled layerwise analysis of thermopiezoelectric composite beams

Previously developed discrete layer mechanics are extended to incorporate thermal effects to account for the complete coupled mechanical, electrical, and thermal response of piezoelectric composite beams. Thermal effects in both the elastic and piezoelectric media are captured at the material level. This unified representation leads to an inherent capability to model both the sensory and active responses of piezoelectric composite beams in thermal environments. Finite element equations are developed and implemented for a beam element with linear shape functions. Results from the current formulation are compared with results from a conventional thermoelastic finite element analysis and classical beam theory. Additional numerical studies demonstrate capabilities of the current formulation to predict the thermal deformation of composite beams, as well as the active compensation of these thermal deformations using piezoelectric structures. The corresponding sensory response and the resultant stress state in the piezoelectric composite beam are also presented. [Amn], [Bmn], [Dmn] b [C] {D} [d] {E} [Emn] [e] {F}