Normal Maximum Stress Research Articles

Effect of Al/Ti ratio on the microstructure, texture and incipient plasticity of (CoNiCr0.5)95AlxTiy high entropy alloys

To analyze the incipient plasticity and then optimize the micromechanical behavior of HEAs, the FCC (CoNiCr0.5)95AlxTiy (x = 1, 3, 4 and y = 4, 2,1 (at.%)) HEAs were selected and thermomechanical processed, and corresponding microstructure, mechanical property and incipient plasticity were investigated and discussed. As the Al/Ti ratio changes from 1/4 to 4/1, the average GND of HEAs decreases from 1.11 × 1014 m−2 to 1.05 × 1014 m−2, and the contents of the A {110} <111> and CopperTwin {552} <115> reach to 11% and 4.4%, respectively. Meanwhile, the ductility of HEA increases from 10.6% to 13.9% with the increased Al/Ti ratio, while the strength decreases from 1221.1 MPa to 910.3 MPa. Nanoindentation results show that the normalized maximum stress τmax/μ of the HEAs exhibit the value of (1/18–1/12)μ, and the average activation volume v∗are calculated to be 3.2–3.4 Ω. These indicate that the incipient plasticity of (CoNiCr0.5)95AlxTiy possesses heterogeneous dislocation nucleation triggered by cooperative migration of multiple atoms via vacancies.

Equations for gap-spanning design of underground cast iron pipes lined with thermosetting polymeric liners

Polymeric spray and cured-in-place-pipe liners have attracted the attention of water utilities as alternatives for renovation of deteriorated cast iron pipes. Circumferential defects, in the form of existing gaps, ring fractures or failed joints, may exist in cast iron pipes and they may significantly influence the performance of the lined pipes under applied loads. Literature review showed that limited research has been conducted to investigate the effect of circumferential defects. This paper aims to comprehensively examine the mechanical performance of polymer lined cast iron pipes with circumferential defects, using finite element analyses, and derive equations based on the finite element results for engineering design. Three different failure modes, namely, lining through existing gaps in pressurized host pipes, formation of gaps for pressurized lined pipes subjected to axial movements, and pressurized lined pipes with ring fractures under bending, are comprehensively studied. After validation of the developed numerical models for each of the failure modes, parametric studies were conducted considering different pipe properties, liner properties, loading conditions and interface properties. Equations were then derived based on the numerical results using non-linear regression for the three failure modes to facilitate the use of the results in practice. It was found from this study that for all three modes a reduction in the ratio of the cast iron pipe modulus to liner modulus will result in an increase in the normalized maximum stress, which is defined as the ratio of the maximum stress to internal pressure in the liner. This effect is most significant for formation of gaps for pressurized lined pipes subjected to axial movements and pressurized lined pipes with ring fractures under bending. It was also found that by increasing the friction coefficient or reducing the ratio of liner wall thickness to pipe diameter, the normalized maximum stress in the liner increases. Among the three failure modes, the normalized maximum stress in the liner for formation of gaps for pressurized lined pipes subjected to axial movements was affected the most.

Design of rectangular industrial duct plates subjected to out-of-plane pressure considering nonlinear large deformations

Large industrial steel ducts are often rectangular and are built-up of stiffened plates. The plates along with stiffeners act to resist the pressure loads and transfer these loads to the supports. Parallel wide flange steel profiles, usually beams, are used as transverse stiffeners that are spaced perpendicular to the longitudinal axis of duct. The design process involves determining the load carrying capacity and deflection of the plate based on the plate thickness and the spacing between stiffeners. The current analysis and design method for industrial ducts is based on the elastic large deflection plate theory using standard tables.A nonlinear finite element parametric study was conducted on dimensionless parameters to investigate the behavior of laterally loaded long plates. Through-thickness yielding of the plate and formation of partial plastic hinges at the ends is allowed. The results are presented in terms of a proposed dimensionless Normalized Load Factor (NLF) representing the applied pressure, the Normalized Deflection Factor (NDF) representing the out-of-plane deflection and the Normalized Maximum Stress Factor (NMSF) representing the maximum stresses induced in the plates. Design equations for deflection and stresses of plates are established with the aid of Bezier curves. A simple design procedure allowing for large deflection and partial yielding of edges is proposed. A limiting value for pressure has been found where it becomes irrelevant to check deflection. Results show that the proposed design procedure is simple and can lead to economic plate thicknesses and spacing of stiffeners in industrial ducts in ambient temperatures.

Modeling the low-cycle fatigue behavior of visco-hyperelastic elastomeric materials using a new network alteration theory: Application to styrene-butadiene rubber

Although several theories were more or less recently proposed to describe the Mullins effect, i.e. the stress-softening after the first load, the nonlinear equilibrium and non-equilibrium material response as well as the continuous stress-softening during fatigue loading need to be included in the analysis to propose a reliable design of rubber structures. This contribution presents for the first time a network alteration theory, based on physical interpretations of the stress-softening phenomenon, to capture the time-dependent mechanical response of elastomeric materials under fatigue loading, and this until failure. A successful physically based visco-hyperelastic model is revisited by introducing an evolution law for the physical material parameters affected by the network alteration. The general form of the model can be basically represented by two parallel networks: a nonlinear equilibrium response and a time-dependent deviation from equilibrium, in which the network parameters become functions of the damage rate (defined as the ratio of the applied cycle over the applied cycle to failure). The mechanical behavior of styrene-butadiene rubber was experimentally investigated, and the main features of the constitutive response under fatigue loading are highlighted. The experimental results demonstrate that the evolution of the normalized maximum stress only depends on the damage rate endured by the material during the fatigue loading history. The average chain length and the average chain density are then taken as functions of the damage rate in the proposed network alteration theory. The new model is found to adequately capture the important features of the observed stress–strain curves under loading–unloading for a large spectrum of strain and damage levels. The model capabilities to predict variable amplitude tests are critically discussed by comparisons with experiments.

The Healing Effect of Bone Morphogenic Protein with Fibrin Glue on an Injury of the Tendon-Bone Junction

Purpose : The author hypothesizes that exogenously injected BMP, which is mixed with fibrin glue, can accelerate the healing of a bone-tendon junction injury and increase its holding strength during the early regeneration period. Materials and Methods : A direct injury model of the bone-tendon junction was made using the Achilles tendon-calcaneus bone of 54 rabbits: and the transected Achilles tendon was repaired to its original insertion site using the Krackow method. In Group 1, no additional manipulation was performed. In Group 2, only fibrin glue was injected into the junction between the Achilles tendon and the calcaneus in order to exclude the effect of the fibrin glue. In Group 3, BMP-2 incorporated into the fibrin glue was injected into the junction. The results were evaluated by histological analysis and biomechanical tests at 2, 4, and 8 weeks after surgery. The Kruskal-Wallis test was used for a statistical evaluation. Results : Histological analysis revealed the early appearance of fibrocartilage at 2 weeks in Group 3: the area of the fibrocartilage expanded with time. The biomechanical tests showed significant differences in the maximum stress between Groups 1 and 3, and between Groups 2 and 3, at 2, 4, and 8 weeks. 74.4% of the normal maximum stress was recovered at 8 weeks in Group 3. Conclusion : The combined use of BMP-2 and the fibrin glue can accelerate the healing of an injury of the bone-tendon junction.

Fatigue behaviour of graphite and interpenetrating graphite–aluminium composite up to 10 9 load cycles

Fatigue behaviour of polycrystalline, isotropic graphite FU2590 (porosity 13 vol%) and of FU2590 infiltrated with the aluminium alloy AlSi7Mg (FU2590/AlSi7Mg) is investigated. The interpenetrating graphite–aluminium composite is produced by squeeze casting infiltration, where the open porosity of FU2590 (10–11 vol%) is infiltrated with AlSi7Mg. Fully reversed bending fatigue tests at cycling frequency 25 Hz and fully reversed tension–compression experiments at 20 kHz are performed. Fatigue data of FU2590 measured with both methods are comparable when presented vs. the normalized maximum stress, i.e. maximum tension stress of a cycle divided by the bending or tensile strength, respectively. The mean endurance limit of FU2590 at 10 9 cycles under tension–compression loading is at 23.0 ± 0.9 MPa (normalized maximum stress 0.65 ± 0.03), and 26.1 ± 1.5 MPa (normalized maximum stress 0.55 ± 0.03) is found for FU2590/AlSi7Mg. The increased endurance limit of FU2590/AlSi7Mg is mainly caused by the 15% higher stiffness compared with FU2590. In reversed bending experiments, at cycles to failure below 10 7, the composite shows about 30% higher cyclic strength. The beneficial influence of infiltration on static properties is more pronounced, and 50% higher bending strength and 35% higher tensile strength are determined. In the graphite, fatigue cracks predominantly initiate at porosity. In the composite, cracks initiate at pores, which are filled with AlSi7Mg. Interface failures and failures of the aluminium alloy limit the beneficial influence of infiltration on the cyclic properties.

Plantar soft tissue loading under the medial metatarsals in the standing diabetic foot

Diabetes mellitus (type 2) is the most frequent cause of non-traumatic lower-limb amputations. The major cause of impairment to the feet of diabetics is persistent hyperglycemia, potentially leading to peripheral neuropathy as well as to pathological changes in plantar soft tissue, which stiffen its structure and diminish its ability to effectively distribute foot–ground contact loads. In this study, a computational model of the foot structure in the standing position was utilized to evaluate stress distributions in plantar soft tissue under the medial metatarsal heads of simulated diabetic versus normal feet. The model comprises five anatomic planar cross-sections in the directions of the foot rays, which were solved for internal stresses under static ankle joint reaction (300 N) and triceps surae muscle forces (150 N) using the finite element method. Tissues were assumed to be homogenous, isotropic and elastic materials, with nonlinear stress-strain relations for the ligaments, fascia and plantar tissue. The model revealed significant tension stress concentrations (90–150 KPa) in the plantar pad of the simulated diabetic forefoot: they were four times the normal maximum stress under the first metatarsal head and almost eight times the normal maximum stress under the second metatarsal head. It was shown that with increased severity of stiffening of the plantar pad, as related to glucose-exposure, peak forefoot contact stresses may rise by 38 and 50% under the first and second metatarsal heads, respectively. The increase in averaged (von Mises) internal stresses within the plantar soft tissue is even more pronounced, and may rise by 82 and 307% for the tissue under the first and second metatarsal heads, respectively. These results, which conform to experimental data gathered over the last two decades, suggest that the process of injury in diabetic feet is very likely to initiate not on the skin surface, but in deeper tissue layers, and the tissues underlying the distal bony prominences of the medial metatarsals are the most vulnerable ones.

Pulsating Stress Controlled Low Cycle Fatigue Behavior of Ti-6Al-4V Alloy at Cryogenic Temperature.

Pulsating low cycle fatigue tests of Ti-6Al-4 V alloy which is thought to be a candidate of structural material at cryogenic temperature have been conducted in a stress controlled condition at 77 K and room temperature. Attention was paid to the S-N relation using normalized maximam stress and changes in cumulative plastic strain and plastic strain range during fatigue. The normalized maximum stress was found to be a key parameter by which the difference of test condition, such as temperature, or the deviation of material property can be evaluated in the same S-N relation. The fracture type of this alloy was found to be divided into quasi-static fracture and fatigue fracture respectivily depending on the magnitude of applied load. This was verified by fracture surface observations. It was found that the resistance to failure in the criteria of both stress and strain at 77 K is higher than that at room temperature.

Strength and life in thermoplastic composite laminates under static and fatigue loads. Part I: Experimental

The static and fatigue characteristics of strength, life, elastic constants and failure mode in AS4 carbon/PEEK (polyetheretherketone) APC-2 laminates were investigated. The laminates, made according to the diaphragm forming method and optimum consolidated process, could be divided as unidirectional, cross-ply and quasi-isotropic 16-ply laminates. Static tensile and compressive tests were conducted to yield the basic material properties and strength. For undirectional and multi-angled laminates the predicted values are close to the empirical data by using the analytical formulations and classical lamination theory. Hence the static tensile and compressive data provide the base-line reference. Our main work, however, is emphasized on fatigue tests subjected to tension–tension (T–T) and compression–compression (C–C) cyclic loadings of constant stress amplitude at room temperature and moisture. The stress ratios were equal to 0 and 0.2 for T–T, and 5 and −∞ for C–C testing at a frequency of 5 Hz. The normalized maximum stress vs. log cycles ( r–log N) curves were plotted systematically to yield the respective fatigue strength at the specific life by interpolation. The predicted fatigue strength by power law of the S– N relation agreed well with the measured data, i.e. the power law is satisfactorily acceptable. The failure modes for multi-angled laminates are more complicated than undirectional laminates for both static and fatigue tests. All these valuable data will be used to predict fatigue strength and life in association with the extended Tsai–Hill fatigue failure criterion in Part II: formulation.

A Simple Model for Fatigue Crack Growth Near Stress Concentrations

Fatigue crack growth rates are often difficult to predict for short cracks growing near stress concentrations. This paper presents a simple model to predict those growth rates which incorporates the phenomenon of crack closure. Crack opening stresses are shown to change significantly as cracks grow away from notches, and the simple model is designed to describe those changes. The effective stress range ratio, U, is assumed to be dependent on the local stress at the crack tip location in a corresponding uncracked body. The value of U changes with the normalized maximum stress in unnotched bodies, and this dependence can be quantified with elastic-plastic finite element models or simpler modified-Dugdale crack analyses. The local stress distribution is estimated with a Neuber analysis. A semi-empirical stress intensity factor solution is constructed and calibrated with known exact solutions. The crack growth rate is then calculated with the modified Paris law, taking crack growth constants from long crack data. The model is illustrated with a specific case study, the growth of cracks from center notches in an SAE 1026 steel. Experimental crack growth data for notches of different sizes and shapes compare favorably with the calculations. The scheme is contrasted with previous models for notch fatigue cracks. The implications of the simple model for other fatigue design problems are explored, highlighting the simplicity and generality of the model.

Effect of stress ratio on tension and delamination fatigue behavior in CF/epoxy laminates

The effect of stress ratio on tension-tension fatigue behavior and mode I delamination fatigue crack propagation behavior was investigated for Toray T300/#3601, T800/#3601 and T800/#3631 laminates. Unidirectional laminates and quasi-isotropic laminates were used for tension-tension fatigue tests. For delamination fatigue crack propagation tests, double cantilever beam specimens made of unidirectional laminates were used. For the tension fatigue tests, the slope of the relation between the normalized maximum stress and the number of cycles to failure was very small. For delamination fatigue crack growth tests, the exponent of the power function in the relation between the crack propagation rate and the stress intensity range was very large. The analysis of the equivalent stress intensity range proposed by the authors showed that the contribution of the maximum stress was large in delamination fatigue crack propagation. A similar analysis was applied to the results of the tension fatigue tests. The contribution of the maximum stress was also large in tension fatigue fracture. The degree of the contribution of the maximum stress in the tension fatigue tests was almost the same as that in the delamination fatigue crack growth tests. A comparison between the mechanism of tension-tension fatigue fracture and that of delamination fatigue crack growth was made on the basis of the fractographic observation.