Maximum Principal Tensile Stress Research Articles

Predictive modelling of the mechanical properties of rubber-toughened epoxy

Introduction Single-phase epoxy polymers are usually relatively brittle materials and are frequently toughened by the incorporation of a rubbery phase [1]. Two important toughening mechanisms have been identified for such two-phase materials, which consist of a rubbery phase dispersed in a matrix of a cross-linked polymer. The first is localized shear yielding, or shear banding, which occurs between rubbery particles at an angle of approximately + 45 ° to the direction of the maximum principal tensile stress [1-3]. Due to the large number of particles involved, the volume of thermoset matrix material which can undergo plastic yielding is effectively increased compared to the single-phase polymer. Consequently, far more irreversible energy dissipation is involved and the toughness of the material is improved. The second mechanism is the internal cavitation, or interfacial debonding, of the rubber particles, which then enables the subsequent growth of these voids by plastic deformation of the epoxy matrix [1-4, 5]. This irreversible hole-growth process of the epoxy matrix also dissipates energy, and so contributes to the enhanced fracture toughness. Recently, attempts [4, 5] have been made to model the toughening mechanisms and this work has clearly demonstrated the importance of establishing a sound finite element analysis representation of the effects of the rubbery phase on the properties of the rubber-toughened polymer. Indeed, this is the aim of the present work, and some most interesting initial results are the subject of the present letter. Predictive modelling of particulate-filled composite materials has frequently been based on the assumption that the material consists of a collection of cylinders, each containing a sphere at its centre [4, 6, 7]. The size of the cylinders as a function of the overall volume fraction can be deduced from assuming a uniform array [4, 6], or assuming a random array [7]. Such analysis is relatively straightforward since the constraints required to model the interactions of surrounding particles may be simply applied by forcing the sides of the cylinder to remain straight. However, this material model is inherently inaccurate since it does not reflect the overall isotropy of the material. The more accurate material model used in the present work is a collection of spheres, each consist-

Optimization of diamond anvil cell performance by finite element analysis

Many diamonds used as anvils in diamond anvil cells fail at the base due to a concentration of tensile stress in this region. The authors have calculated the maximum principal tensile stresses in the lower half of the anvil and in the support for simulated anvil plus support finite element meshes. The Young's modulus E and Poisson's ratio v for both components were varied systematically. Geometrical parameters determining the shape of the light port in the support and the shape of the anvil were also varied. The effect of geometry in minimizing or enhancing basal tension is profound. There is a well defined tension minimum for a conical light port of semi-angle 25-30 degrees . Simulations were also calculated for a diamond on a flat B4C plate. Such supports often fail at low pressure (around 3.5 GPa). The tension in the support decreased rapidly for a small increase in plate thickness.

Use of reference stress to correlate creep fracture lifetimes of monolithic ceramics in uniaxial tension and flexure

Most of the very limited tensile creep information on monolithic ceramics has been generated using the four point bend test. Where data on ceramics under uniaxial tension do exist, it is invariably the case that lifetimes are much longer under flexure when, as is usual, the maximum principal tensile stress is used as the correlating parameter. In this paper, creep lifetime data for hot pressed silicon nitride are used to demonstrate that a geometry dependent ‘reference stress’ is a much superior correlating parameter and that its successful usage leads to important deductions about the process of fracture in this class of materials, under the stress and temperature regime studied.MST/1668

Use of reference stress to correlate creep fracture lifetimes of monolithic ceramics in uniaxial tension and flexure

Most of the very limited tensile creep information on monolithic ceramics has been generated using the four point bend test. Where data on ceramics under uniaxial tension do exist, it is invariably the case that lifetimes are much longer under flexure when, as is usual, the maximum principal tensile stress is used as the correlating parameter. In this paper, creep lifetime data for hot pressed silicon nitride are used to demonstrate that a geometry dependent ‘reference stress’ is a much superior correlating parameter and that its successful usage leads to important deductions about the process of fracture in this class of materials, under the stress and temperature regime studied.MST/1668

Pellet crack mechanism at power ramps

A pellet crack mechanism has been established when power ramp occurs. Two possible cases with initial pellet cracks are considered in this work. In the first case, initial crack tips are assumed to exist in the cracked pellet and the strain energy density function is applied as the pellet fracture criterion. In the second case, “gaps” among the pellet fragments are simulated for crack pattern and the maximum tensile principal stress is used as failure criterion. Most of the PCMI models have been reviewed and the derived interfacial stress states are used to prescribe the boundary conditions of the fuel pellet which are clarified as uniform contact, linearly varying contact and bonding. Both the crack propagation and fracture initiation are expected for the three types of contact in the present work. Generally speaking, crack will propagate in the circumferential direction for the first case study, while fracture is initiated at the midplane between the two adjacent cracks for the second case study. The results presented here are in agreement with the experimental observation. Fission gas release related to the pellet crack at power ramps is also discussed.

Nonlinear dynamic response of window glass plates subjected to fluctuating wind pressures

It is common practice to analyze and design window glass units using an equivalent static wind pressure. Little is known with regard to the dynamic behavior of window glass units subjected to a fluctuating wind pressure. Here, a mathematical model is developed to determine this dynamic behavior. A random fluctuating wind pressure is simulated using the well known Davenport spectrum for wind velocity and Vaicaitis expression for generating discrete wind velocity-time data. For the analysis of the plate, the dynamic nonlinear von Karman plate equations are used. The dynamic finite difference model developed by Vallabhan and Selvam is modified to consider the response due to sample fluctuating wind pressures. Time dependent displacement and maximum tensile principal stress in two vibrating glass plates are the outcome of this analysis.

FEM Modeling of Fictitious Crack Propagation in Concrete

Using a mixed‐mode extension of the Hillerborg fictitious crack model, a practical interface finite element approach is used to model discrete crack propagation. The fictitious crack tip propagates perpendicular to the maximum tensile principal stress at its tip when the tensile strength is exceeded. A dynamic relaxation method is employed. Interface elements have been used before to model such cracks; however, the software technology is in a state of rapid development, making possible improvements in the modeling of discrete nonlinear crack propagation. The concept of fracture process zone is broadened to one of interface process zone, which includes the nonlinear behavior of the fracture process zone as well as the crack face interference behind the fracture process zone. A development makes the method efficient while preserving the accuracy of the fictitious crack model. The fictitious crack is represented by interface elements with linearly varying displacements; however, the traction distribution is arbitrary. As example problems demonstrate, these assumptions allow the fictitious crack to be modeled using few degrees of freedom without compromising accuracy. Modeling of the size effect is presented.

Micromechanical modeling of healed crack orientations as a paleostress indicator: Application to Precambrian granite from Illinois and Wisconsin

We have used a micromechanical, four‐grain model to simulate intragranular cracks produced during primary cooling of a granitic pluton in a horizontally anisotropic stress field. The orientations of vertical, intragranular cracks were obtained using the criterion that they are perpendicular to the maximum principal tensile stress when it exceeds the local tensile strength. The preferred orientation was always parallel to the maximum regional compressive stress direction. The sharpness of the distribution peak increases with the ratio of the maximum to minimum horizontal stress. We applied the model results to new and previous data on Precambrian granites from Wisconsin and Illinois. Our new data are healed crack orientations and fluid inclusion properties in unoriented granite core from Illinois borehole UPH‐2. The fluid inclusion measurements and isotopic age dates indicate that most healed cracks were formed during the primary cooling of the pluton. The fluid inclusion characteristics and shape of the crack orientation distribution were almost identical to those previously determined for UPH‐3, 1 km away (Kowallis et al., 1987), suggesting that the preferred orientation of healed cracks in granite from UPH‐2 is the same as for UPH‐3 (N25°W ± 5°). The orientation distribution from the micromechanical model for a stress ratio of 4 is very similar to the healed crack orientation distribution measured in several Precambrian granites from the midcontinent region. We conclude that healed crack orientations are useful indicators of the paleostress field and that they may be used as a tool for orienting core in stable, structurally simple regions.

Evaluation of Low‐Cycle Fatigue Strength of Structural Metals

Better understanding of the multiaxial low‐cycle fatigue strength of structures and/or components is important for the design of structures under severe repeated loading. Significant discrepancies exist between experimental results and currently available analytical predictions. This paper presents a method to evaluate the low‐cycle fatigue strength of structural metals based on a plastic work concept. The maximum principal tensile stress is incorporated into the evaluation as a second parameter to account for the progressive failure characteristics. This proposed approach narrows the scatter band of low‐cycle fatigue life predictions, and is convenient for engineering applications. The two necessary parameters in this evaluation method, the plastic work per cycle and the maximum tensile principal stress, can be obtained by experiments or by using theoretical constitutive modeling. In this study, they have been obtained through theoretical calculations and validated by experimental data. Also illustrated in this paper is a relatively simple design procedure using the proposed method.

Criteria for Crack Nucleation in Polycrystalline Ice

A theoretical analysis of crack nucleation in isotropic polycrystalline ice due to the elastic anisotropy of the constituent crystals has recently been presented by Shyam Sunder and Wu [1]. Subsequently, Shyam Sunder and Nanthikesan [2] have analyzed crack nucleation in polycrystalline ice that is isotropic but porous. The singularity of the stress concentrations near a grain boundary facet junction provides the mechanism for inducing microcrack precursors, if similar nuclei do not already exist. The total stress field is obtained by linearly superposing the microstructural stress field created by the elastic anisotropy mechanism on the applied stress field. Assuming plane stress conditions, the analysis of the nucleation stress is based on a solution to the problem of an extending precursor in a combined stress field including the effects of Coulombic frictional resistance. In the earlier papers, the local material resistance is characterized in terms of a critical value for the maximum principal tensile stress, MPTS, (Erdogan and Sih [3]). This paper compares the nucleation stresses for uniaxial and biaxial loading conditions obtained previously with those obtained from the use of a critical strain energy density, SED, factor (Sih [4]) to characterize the local material resistance. The results, synthesized into biaxial nucleation surfaces, are compared with the limiting tensile strain, LTS, criterion of Shyam Sunder and Ting [5]. The critical precursor orientation and the incipient growth direction for the two models are also compared.

A creep rupture model accounting for cavitation at sliding grain boundaries

An axisymmetric cell model analysis is used to study creep failure by grain boundary cavitation at facets normal to the maximum principal tensile stress, taking into account the influence of cavitation and sliding at adjacent inclined grain boundaries. It is found that the interaction between the failure processes on these two types of adjacent facets reduces the failure time significantly when cavitation is creep constrained. In all cases the time to cavity coalescence on transverse facets appears to be a useful lower bound measure of the material life-time. Sliding at the boundaries of the central grain of the cell model is accurately represented; but in some computations a stress enhancement factor is used to incorporate also the effect of sliding between surrounding grains. The influence of grain boundary viscosity is included in the model and it is found that even in the absence of sliding, cavitation on inclined boundaries may significantly reduce the failure time.

Tensile failure of pultruded glass-polyester composites under superimposed hydrostatic pressure

The tensile properties of five types of pultruded 0·52 V f glass-fibre-polyester rods were investigated by extending waisted round specimens at atmospheric and superimposed hydrostatic pressures, −H, to 300 MPa. The maximum principal stress at fracture, −700 MPa, decreased, with the superimposition of −H, approximately by its magnitude. As −H increased the failure surfaces became flatter, the amount of fibre pull-out decreased and transverse cracks became shorter or were eliminated. Glass fibres in the failure surfaces were resin free, and failure of the glass fibre bundles appeared to control the fracture process in the entire pressure range for all materials. The decrease in maximum principal tensile stress with increasing −H indicates that the glass fibre failure process is not controlled by a critical tensile stress. Failure criteria are discussed, and in the tension-compression-compression octant of stress space the relevant criteria appear to be strain energy and deviatoric tensile stress, strain and strain energy for these GRPs and glass itself.

金属焼付ポーセレン冠の破折に関する実験的研究

Ceramo-metal restorations have been extensively used because of their superior strength, esthetics and stability. However, fractures are sometimes encountered in ceramo-metal crowns. This study was designed, therefore, to evaluate the fracture strength of ceramo-metal crowns in relation to the material and design of metal coping, and mode of loading by means of fracture test and two-dimensional finite element analysis. A gold alloy and a nickel-chromium alloy were employed as the coping material. The designs of the crown were type A with the metal frame being bare by cervical one third ; type B with the metal frame being bare by cervical two thirds ; and type C with the metal frame being almost all bare in the lingual surface. The results were summarised as follows : 1. When the compressive load was applied to the incisal edge along the tooth axis, type C showed the lowest fracture strength and no significant difference was found between type A and B. The gold alloy coping offered higher strength than the nickel-chromium alloy coping. 2. When the load was applied in 45° to the tooth axis, there were no significant differences among the coping designs and materials. 3. In the finite element analysis, the estimated peak and distribution of the maximum principal tensile stress were in good agreement in their tendencies with the results of the fracture tests. 4. Further stress analysis with the finite element method showed that the potentiality of fracture in the porcelain increased as the loading point was shifted from incisal edge to cervical side. Such a tendency was especially marked in type C. 5. In considering the normal occlusion, however, very low level of tensile stress was introduced in type C because the load was to be directed to the metal coping. 6. The estimated residual stress in the porcelain caused by the thermal stress during cooling process was higher in the nickel-chromium alloy coping and type C, which may promote the fracture of the ceramo-metal crown. 7. From the foregoing findings, it is recommended to minimize the fracture that the metal backing should not be too large when the occlusal force is applied to the porcelain itself.

Crack nucleation due to elastic anisotropy in porous ice

This paper presents a theoretical analysis of crack nucleation in isotropic but porous ice due to the elastic anisotropy of the constituent crystals. Samples of freshwater polycrystalline ice made in the laboratory and those found in nature are in general porous materials. Even relatively dense samples of laboratory ice contain bubbles with average diameters in the range of 0.06–0.12 mm and average bubble densities of 350−6500 bubbles-cm −3. Concentrated stress fields are produced both due to geometrical discontinuities such as grain-boundary-facet junctions and the presence of the pores which are often located in the vicinity of grain boundaries. The singularity of the microstructural stress field produced by crystal anisotropy provides the mechanism for inducing microcrack precursors on the surface of the pores, if similar nuclei do not already exist. Formation of the precursor relieves the stress singularity and a first-order approximation is adequate to characterize the remaining microstructural field. The precursors can nucleate into microcracks through the local intensification of the concentrated stress field around the pore produced by the applied stresses and the first-order microstructural stresses. The analysis of the nucleation stress is based on a solution to the general problem of an extending precursor in a combined stress field including the effects of Coulombic frictional resistance. The local material resistance is characterized in terms of a critical value for the maximum principal tensile stress which can be determined from the surface free energies of either the grain boundary or the solid-vapor interface. The stress gradients acting along the plane of the precursor due to the presence of the pore are taken into account in modeling frictional effects and computing the stress-intensity factors. Model predictions for relatively dense polycrystalline ice show that: (i) the presence of the pore influences the nucleation stresses at smaller grain sizes, i.e., less than about 5 mm, where the precursor and pore become comparable in size; (ii) the stress required to nucleate cracks in compression varies between 2.25–3.60 times that in tension, the larger values occur as the grain size decreases below 5 mm; (iii) the nucleation stress in tension closely follows the well-known linear Hall-Petch relationship with the inverse square root of grain size exhibited by experimental data; (iv) the stress required to nucleate a crack in compression is strongly dependent on crystal orientation and, as a consequence of the random orientation of crystals in isotropic polycrystalline ice, there can be a distinct beginning and end to the microcrack-nucleation phase when stress is increased and if failure does not occur prematurely; (v) the pore serves to change the nature of first crack nucleation from a shearing or mixed-mode phenomenon to a tension-dominated phenomenon as the grain size decreases below 5 mm, and this tends to align the microcracks perpendicular to the loading axis in tension and parallel to it in compression; (vi) a generalization of the limiting tensile-strain criterion proposed by Shyam Sunder and Ting (1985) which accounts for the anisotropy of the constituent crystals is an adequate phenomenological approximation of the nucleation surface under multiaxial states of stress.

Crack nucleation due to elastic anisotropy in polycrystalline ice

This paper presents a theoretical analysis of crack nucleation in isotropic polycrystalline ice due to the elastic anisotropy of the constituent crystals. The singularity of the associated stress concentrations near a grain-boundary facet junction provides the mechanism for inducing microcrack precursors, if similar nuclei do not already exist. The first-order microstructural stress field created by the elastic anisotropy mechanism is linearly superposed on the applied stress field. This total stress field causes the precursors to nucleate into microcracks. The analysis of the nucleation stress is based on a solution to the general problem of an extending precursor in a combined stress field including the effects of Coulombic frictional resistance. The local material resistance is characterized in terms of a critical value for the maximum principal tensile stress which can be determined from the surface free energy of either the grain boundary or the solid-vapor interface. Model predictions show that: (a) the stress required to nucleate cracks in compression is about 2.5 times that in tension, unlike other microstructural models which predict them to be equal; (b) elastic anisotropy rather than dislocation pile-up as proposed by others may govern crack nucleation in tension over a wide range of strain rates; (c) the stress required to nucleate a crack in compression is strongly dependent on crystal orientation and, as a consequence of the random orientation of crystals in isotropic polycrystalline ice, there can be a distinct beginning and end to the microcrack nucleation phase when stress is increased and if failure does not occur prematurely; (d) the grain size effect due to the elastic anisotropy mechanism is similar to that due to the dislocation pile-up mechanism over the typical range of grain sizes encountered in nature; and (e) a generalization of the limiting tensile strain criterion ∗ ∗ Proposed by Shyam Sunder and Ting (1985). which accounts for the anisotropy of the constituent crystals is an excellent phenomenological approximation of the nucleation surface under multiaxial states of stress.

Sliding contact fracture on glass and silicon

Surface crack geometry produced during sliding contact on amorphous glass specimens and silicon single-crystal specimens was investigted. The experiments were performed by sliding a spherical indentor on a surface with increasing normal load in ambient air and oil environments. The results show that the cracks formed on the contact surface due to sliding motion are governed by the stress field generated. Cracks tend to follow the maximum principal tensile stress trajectories in amorphous glass specimens, but the cracks generated on silicon were strongly influenced by the planes of easy cleavage on the contact surface. The normal load P, friction coefficient of contact and crystallographic cleavage plane directions were found to have a large influence on the surface crack patterns. A general relation, W ∝ P1/3, was obtained for the measurement of crack widths W in all testing conditions. Crack-morphologies were related to material removal. Studies showed that the latter is often due to chip formation which occurs between very closely spaced cracks.

Micromechanisms of deformation in polyethylene

It is widely accepted that crazes form in polymers on a plane which is always normal to the direction of maximum principal tensile stress, and indeed this is a tenet of the fundamental theory of the growth and formation of crazes. However, Harris and Ward [1] reported the appearance of crazes (when re-drawing oriented polyethylene terephthalate) which appeared to form at various angles to the direction of the applied maximum principal tensile stress. On the other hand, Brady and Yeh [2] supposed the crazes observed by Harris and Ward to be formed by the cracking open of preformed shear bands, due to the opening component of the applied tensile stress, upon re-drawing. Brady and Yeh [2] considered the question of whether the features observed by Harris and Ward were "shear bands", or "shear crazes" to be semantic. However, the processes which give rise to shear bands and shear "crazes" are fundamentally different, in that shear processes tend to occur without a change in volume of the material undergoing deformation whereas crazing involves dilatation. Thus, if it is proposed that a craze forms due to the component of deviatoric stress, this assertation must be justified by proposing a mechanism which can cause dilatation purely under the action of an applied shear stress. Indeed, the author has proposed a continumn model for the stress system in which a shear craze can form [3]. However, although proposing a mechanism for the formation of such a craze, that mechanism is not wholly satisfactory since it does not specify the way in which voids can grow due to the deviatoric component of the applied stress, and therefore does not distin-

A hypothesis on the mechanism of trauma of lung tissue subjected to impact load.

When a compressive impact load is applied on the chest, as in automobile crash or bomb explosion, the lung may be injured and show evidences of edema and hemorrhage. Since soft tissues have good strength in compression, why does a compression wave cause edema? Our hypothesis is that tensile and shear stresses are induced in the alveolar wall on rebound from compression, and that the maximum principal stress (tensile) may exceed critical values for increased permeability of the epithelium to small solutes, or even fracture. Furthermore, small airways may collapse and trap gas in alveoli at a critical strain, causing traumatic atelectasis. The collapsed airways reopen at a higher strain after the wave passes, during which the expansion of the trapped gas will induce additional tension in the alveolar wall. To test this hypothesis, we made three new experiments: (1), measuring the effect of transient overstretch of the alveolar membrane on the rate of lung weight increase; (2) determining the critical pressure for reopening collapsed airways of rabbit lung subjected to cyclic compression and expansion; (3) cyclic compression of lung with trachea closed. We found that in isolated rabbit lung overstretching increases the rate of edema fluid formation, that the critical strain for airway reopening is higher than that for closing, and that these critical strains are strain-rate dependent, but independent of the state of the trachea, whether it is open or closed. Furthermore, a theoretical analysis is presented to show that the maximum principal (tensile) stress is of the same order of magnitude as the maximum initial compressive stress at certain localities of the lung.(ABSTRACT TRUNCATED AT 250 WORDS)

Thermoelastic analysis of radiation-heating thermal shock

AbstractA thermoelastic model consisting of an infinite slab-type rectangle symmetrically heated on two faces with a constant heat transfer coefficient is used to interpret radiationheating thermal shock experimental results. The solution of the maximum principal tensile stress of the model is presented in dimensionless form, and a graphical method of inverting the stress solution is described and used to construct the loci of fracture initiation curves that highlight the transient aspect of the thermal stress fracture problem. A solution for the total strain energy is also presented and a method for computing the elastic strain energy at fracture is described. Previously reported thermal shock data are interpreted in terms of a thermoelastic damage-resistance parameter that accounts for the combined effects of material properties, geometry and thermal loading.

Thermal stress fracture of refractory lining components: Part I. Thermoelastic analysis

This paper presents a mathematical model and corresponding stress analysis suitable for the development of theoretical criteria useful for the design and selection of refractory components of linings of high-temperature furnaces and metallurgical process vessels. Refractory lining components, for which the maximum principal tensile stress fracture criterion is assumed valid, are simulated using a two-dimensional constant heating rate thermoelastic model. Dimensional analysis and the finite element numerical method are utilized to develop a general solution for the maximum principal tensile stress in a rectangular shape of arbitrary length and width in terms of thermal and mechanical properties and heating and cooling rate. Implications of the general stress solution with regard to fracture behavior and design recommendations are discussed with reference to results previously reported in the literature.