Mechanical and Industrial Engineering Department

An experimental study was conducted to evaluate notch effects on fatigue behavior of a neat polymer (PP impact co-polymer) and a composite made of 30 wt% short glass fibers in polybutylene terephthalate (PBT). A plate-type specimen geometry with a central circular hole was used. The experiments were conducted at room temperature in uniaxial tension-tension (R = 0.1) and tension-compression (R = -1) loading conditions. Some analytical methods including Neubers rule and the method of critical distances were used in addition to FEA to predict fatigue life of notched specimens. Neubers rule commonly used for metallic materials proved to be an accurate method for predicting the notched fatigue life of the thermoplastics considered.

Applications of short fiber reinforced polymer composites (SFRPCs) have been rapidly increasing and most of the components made of these materials are subjected to cyclic loading. Therefore, their fatigue behavior and modeling have been of much interest in recent years. This literature review presents a broad review of the many factors influencing cyclic deformation, fatigue behavior, and damage development in SFRPCs. These include microstructural related effects as well as effects related to loading condition and their service environment. Microstructural related effects include those related to fiber length, content and orientation, surface treatment, and failure mechanisms. Cyclic deformation and softening, viscous characteristics, and dissipative response used to characterize and model their fatigue damage behavior and accumulation are discussed. The effects of stress concentrations and their gradient on fatigue behavior are also discussed, due to their significant influence. The effects related to the loading condition include mean stress effects which may be accompanied by cyclic creep, variable amplitude loading, and multiaxial stress effects. Since fatigue behavior is substantially influenced by the testing frequency with self-heating as the primary consequence of increased frequency, this effect is also investigated. Environmental effects considered include the effects of moisture content and temperature, as well as thermo-mechanical fatigue behavior. The effect of welded joints in manufactured components made of SFRPCs and fatigue analysis and life estimation techniques used for such components are also included.

An experimental study was conducted to investigateanisotropy effects on tensile properties of two short glass fiber reinforced thermoplastics. Tensile tests were performed in various mold flow directions and with two thicknesses. A shell-core morphology resulting from orientation distribution of fibers influenced the degree of anisotropy. Tensile strength andelastic modulus nonlinearly decreased with specimen angle and Tsai-Hill criterion was found to correlate variation of these properties with the fiber orientation.Variation of tensile toughness with fiber orientation and strain rate wasevaluated and mechanisms of failure were identified based on fracture surface microscopic analysis and crack propagation paths. Fiber length, diameter, and orientation distribution mathematical models were also used along with analytical approaches to predict tensile strength and elastic modulus form tensile properties of constituent materials. Laminate analogy and modified Tsai-Hill criteria provided satisfactory predictions of elastic modulus and tensile strength, respectively.

An experimental study was conducted to evaluate the effect of water absorption on tensile and fatigue behaviors of an impact-modified short glass fiber polyamide-6 and a short glass fiber polybutylene terephthalate. Specimens were prepared in the longitudinal and transverse directions with respect to the injection mold flow direction and immersed in water. Kinetics of water absorption was studied and found to follow the Fick’s law. Tensile tests were performed at room temperature with specimens in the longitudinal and transverse directions and with various degrees of water absorption. Mathematical relations were developed to represent tensile properties as a function of water content. Load-controlled tension-tension fatigue tests were conducted in both longitudinal and transverse directions and correlations between tensile and fatigue strengths were obtained. Specimen fracture surfaces were also microscopically studied and mechanisms of tensile and fatigue failures were identified.

Effects of anisotropy and temperature on cyclic deformation and fatigue behavior of two short glass fiber reinforced polymer composites were investigated. Fatigue tests were conducted under fully-reversed (R = -1) and positive stress ratios (R = 0.1 and 0.3) with specimens of different thicknesses, different fiber orientations, and at temperatures of -40 °C, 23 °C, and 125 °C. In samples with 90° fiber orientation angle, considerable effect of thickness on fatigue strength was observed. Effect of mold flow direction was significant at all temperatures and stress ratios and the Tsai-Hill criterion was used to predict off-axis fatigue strengths. Temperature also greatly influenced fatigue strength and a shift factor of Arrhenius type was developed to correlate fatigue data at various temperatures, independent of the mold flow direction and stress ratio. Micromechanisms of fatigue failure at different temperatures were also investigated. Good correlations between fatigue strength and tensile strength were obtained and a method for obtaining strain-life curves from load-controlled fatigue test data is presented. A fatigue life estimation model is also presented which correlates data for different temperatures, fiber orientations, and stress ratios.

An experimental study was conducted on tensile and fatigue behaviors of two unreinforced polymers and two short glass fiber reinforced polymer composites. A number of effects including anisotropy, strain rate and temperature on tensile behavior was investigated. Fatigue behavior was evaluated with respect to effects of mold flow direction, temperature, mean stress, and stress concentration. Effect of mold flow direction on both tensile and fatigue behaviors of unreinforced materials was found to be negligible, while it was significant for reinforced materials. Tsai-Hill criterion commonly used for continuous fiber composites was used to predict the off-axis fatigue strengths of short fiber reinforced materials. Effect of strain rate on tensile properties was found to be significant for all materials. Test temperature also influenced tensile and fatigue behaviors of both unreinforced and reinforced materials. Mathematical equations were developed to represent variations of tensile properties with both temperature and strain rate. Walker equation with a mean stress correction parameter is proposed to correct for the effect of mean stress. Effect of stress concentration combined with mold flow direction and mean stress was also investigated and Neuber's rule resulted in accurate estimation of fatigue life.

An experimental study was conducted to evaluate the effect of frequency and self-heating on fatigue behavior of two unreinforced and two short glass fiber reinforced thermoplastic polymers. Load-controlled fatigue tests were conducted under fully reversed (R = −1) and R = 0.1 conditions with specimens loaded in either longitudinal or transverse direction to the mold flow direction. Effect of frequency on fatigue life was evaluated at 23 and 125°C and for a range of frequencies between 0.063 and 20 Hz. Incremental step frequency tests were also performed at different stress ratios and stress levels. Surface temperature rise was found to be material, frequency, and stress level dependent. Three energy-based models were applied to the incremental step frequency data and relationships were developed for each material to estimate surface temperature rise as a function of test frequency and stress level. Relationships were also developed to assess critical frequency for the unreinforced thermoplastics at a given stress level above which surface temperature does not stabilize.

An experimental study was conducted to evaluate the effect of mean stress on fatigue behavior of two short glass fiber reinforced thermoplastic composites and the effect of stress concentration on fatigue behavior of an unreinforced and a short glass fiber reinforced thermoplastic. Load-controlled fatigue tests were conducted on unnotched (smooth) specimens at R ratios of −1, 0.1, and 0.3 in different mold flow directions or fiber orientations and at a range of temperatures between −40 and 125 °C. Effect of mean stress on fatigue life was found to be significant at all temperatures. Several mean stress parameters including modified Goodman, Walker, and Smith–Watson–Topper were evaluated for their ability to correlate mean stress data. A general fatigue life prediction model was also used to account for the effect of mean stress, temperature, and fiber orientation. Notched fatigue tests of an unreinforced polymer and a short glass fiber thermoplastic composite were also conducted using plate type specimens with a central circular hole and with or without the presence of mean stress. Effect of stress concentration was found to be considerable, with or without mean stress and in both the longitudinal and transverse directions. The commonly used Neuber's rule for metallic materials, nonlinear finite element analysis, as well as critical distance approaches were utilized for notch deformation and fatigue life analyses.

Cyclic deformation and fatigue behavior of two short fiber thermoplastic composites (SFTCs) under a number of loading and environmental conditions are investigates. The considered environmental effects include those of low and elevated temperatures as well as moisture (or water absorption). Fatigue behavior is also explored under the action of non-zero mean stress (or R ratio) in addition to fully-reversed (R = -1), as well as various cyclic loading frequencies. Material anisotropy and geometrical discontinuity effects (i.e. stress concentration) are other aspects considered in this study. Based on experimental observations and analysis, a number of analytical and empirical models are developed for predicting fatigue behavior under different conditions. Empirical equations are presented to characterize self-heating under cyclic loading. Tsai-Hill criterion is applied to account for the effect of fiber orientation on fatigue life. Mean stress effect is corrected with several mean stress parameters and a shift factor of Arrhenius type is defined to characterize the effect of temperature on fatigue life. Two methodologies are presented to estimate fatigue properties based on tensile properties. Estimation of notched fatigue behavior based on smooth fatigue behavior is also presented.

An experimental study was conducted to investigate the effects of temperature and strain rate on tensile behavior of polybutylene terephthalate and polyamide-6 reinforced with short glass fibers. Tension tests were performed in several mold flow directions, at a range of temperatures between À40 C and 125 C, and a range of strain rates between 5 Â 10 À5 s À1 and 5 Â 10 À1 s À1. Mathematical relationships were developed to represent the stress–strain response, as well as tensile strength and elastic modulus in terms of strain rate and temperature. Time–temperature superposition principle was also employed to superimpose the effect of temperature and strain rate on tensile strength. A temperature-dependent shift factor of Arrhenius type is suggested, which is independent of the mold flow direction. Mechanisms of tensile failure were also identified from fractured surface of specimens.

Cyclic deformation and fatigue behavior of two short fiber thermoplastic composites (SFTCs) under a number of loading and environmental conditions are investigated. The considered environmental effects include those of low and elevated temperatures as well as moisture (or water absorption). Fatigue behavior is also explored under the action of non-zero mean stress (or R ratio) in addition to fully-reversed (R = À1), as well as various cyclic loading frequencies. Material anisotropy and geometrical discontinuity effects (i.e. stress concentration) are other aspects considered in this study. Mechanisms of fatigue failure are also assessed under environmental effects. Based on experimental observations and analysis, a number of analytical and empirical models are developed for estimating fatigue behavior under different conditions. Empirical equations are presented to characterize self-heating under cyclic loading. Tsai-Hill criterion is applied to account for the effect of fiber orientation on fatigue life. Mean stress effect is corrected with several mean stress parameters and a shift factor of Arrhenius type is defined to characterize the effect of temperature on fatigue life. Two methodologies are presented to estimate fatigue properties based on tensile properties, in addition to approximation of strain-life curves based on load-controlled fatigue data. Estimation of notched fatigue behavior based on smooth (un-notched) fatigue behavior is also presented.

Supply chain management is one of the new approaches that are considered significantly by variety of experts and enterprises in today competitive world. Supply chain refers to the network of facilities, supply centers, production centers and distribution centers which encompass various tasks such as providing raw materials, transforming raw materials to components or finished products and distributing them among customers. Regarding this issue, studying literature indicates on this fact that multi-level, multi-product, multi-period models in multi-sourcing situation by considering the supply capacity have not been taken into account notably and just few mathematical models are proposed for the analysis of such decisions. In this paper, it is attempted to investigate and delve into the supply chain planning issue in multi-level, multi-product, multi-period situation. In the proposed model, simultaneously optimization of two objectives is considered which entails maximizing the service level related to giving agreeable services to customers at each retailer's site and minimizing the overall costs of supply chain. As the proposed mixed integer non-linear model has specific complexity, branch and bound solver is utilized and has been applied for a data set in an automotive supply chain. In this way, a model has been presented which determines the lot size of ordering among various members in a supply chain, the amount of holding inventory at each elements of supply chain's site, optimal combination of selecting potential suppliers and the amount of ordering components to suppliers.