A continuous damage approach to the fatigue process

The fatigue process is analyzed theoretically by studying the interaction between a macroscopic crack and continuously distributed microdamage near the crack-tips. A mode I loading case is studied, using a Dugdale crack model. The results show good agreement with Paris' law for fatigue crack propagation with an exponent approximately equal to 4. The model also predicts a finite fatigue lifetime in the sense that the crack growth rate increases without limit after a finite number of load cycles.     

A refined statistical approach to thermal fatigue life prediction

Finding new applications for ceramic materials requires a better knowledge of thermal fatigue behaviour. However, result-scattering inherent to thermal fatigue and duration of a thermal fatigue cycle lead to a lack of experimental results. For these reasons, we have developed a new approach that permits the determination of a relevant stress intensity factor exponent n with a minimum testing sample number. From knowledge of the distribution function of artificial cracks, the analytical formula of the failure probability F(N) can be completely determined. Thus, it is possible to calculate n from a correlation of F(N) with experimental results obtained for only one temperature difference. Correlations between theoretical curves F(N) and experimental results, conducted for two temperature differences, lead to the same value of n. This and the good agreement between the experimental points and the theoretical curves validate this new approach.     

A cohesive model for fatigue failure of polymers

A cohesive failure model is proposed to simulate fatigue crack propagation in polymeric materials. The model relies on the combination of a bi-linear cohesive failure law used for fracture simulations under monotonic loading and an evolution law relating the cohesive stiffness, the rate of crack opening displacement and the number of cycles since the onset of failure. The fatigue component of the cohesive model involves two parameters that can be readily calibrated based on the classical log-log Paris failure curve between the crack advance per cycle and the range of applied stress intensity factor. The paper also summarizes a semi-implicit implementation of the cohesive model into a cohesive-volumetric finite element framework, allowing for the simulation of a wide range of fatigue fracture problems.     

Static fatigue of glass: functional dependence of failure time on stress

Static fatigue of as-received Pyrex borosilicate glass was examined over a wide range of stress and failure time under constant temperature, relative humidity, and surface treatment. It was necessary to calculate the load on the sample from strain guage measurements. The mean log failure time was related to the reciprocal of stress or the reciprocal of stress squared; power law and direct proportionality to stress gave poorer fits.     

A unified theory of fatigue crack growth: a statistical approach

Treating the local fracture toughness of a material as a random value, a general relationship between the applied fracture parameter and the stable crack growth distance is developed. The result is applied to a study of the fatigue crack growth and a general expression connecting fatigue crack growth rate and the applied loading is rendered. Several empirical fatigue crack growth models can be derived on the basis of this unified view, and the valid ranges of these models are established. The conclusions are found to be in agreement with experimental evidence.     

A statistical process control approach to business activity monitoring

Statistical Process Control (SPC) techniques have been successfully used in manufacturing industries to trigger and identify the root cause of variations so as to promote quality improvement. This paper develops a SPC framework to identify important changes deserved in business activity monitoring. To model and track thousands of diversified customer behaviors, the proposed SPC system consists of efficient and robust profiling methods to accommodate different behavior patterns including business changes, structural breakdowns, and unnecessary errors. Several customer profiling techniques are discussed and the activity monitoring performance based on the profiling algorithms is compared in a simulation example and a customer churn detection example in a telecommunications setting. The enhanced system will allow business managers and engineers to establish successful customer loyalty programs for churn prevention and fraud detection.     

Static fatigue and time to failure predictions of particulate filled epoxide resin composites

The long term strength of two composites under constant load has been measured at various temperatures during a period of up to 2 years. Based on the concepts of linear elastic fracture mechanics, times to failure were predicted from short term experiments. The parameters necessary for the analysis were determined using either the double torsion test technique or by measurements of tensile strength at constant stressing rates. It has been found that both procedures lead to nearly equivalent predictions of the static fatigue behaviour of laboratory specimens from room temperature almost up to the glass transition temperature. Deviation of the predictions from experimental long term data are minor and are thus well acceptable for engineering design.     

Molecular design and evaluation of biodegradable polymers using a statistical approach

The challenging paradigm of bioresorbable polymers, whether in drug delivery or tissue engineering, states that a fine-tuning of the interplay between polymer properties (e.g., thermal, degradation), and the degree of cell/tissue replacement and remodeling is required. In this paper we describe how changes in the molecular architecture of a series of terpolymers allow for the design of polymers with varying glass transition temperatures and degradation rates. The effect of each component in the terpolymers is quantified via design of experiment (DoE) analysis. A linear relationship between terpolymer components and resulting T_g (ranging from 34 to 86 °C) was demonstrated. These findings were further supported with mass-per-flexible-bond analysis. The effect of terpolymer composition on the in vitro degradation of these polymers revealed molecular weight loss ranging from 20 to 60 % within the first 24 h. DoE modeling further illustrated the linear (but reciprocal) relationship between structure elements and degradation for these polymers. Thus, we describe a simple technique to provide insight into the structure property relationship of degradable polymers, specifically applied using a new family of tyrosine-derived polycarbonates, allowing for optimal design of materials for specific applications.     

A constitutive model for the viscoplastic behavior of rubbery polymers at finite strains

Summary. A constitutive model is derived for the viscoplastic behavior of rubbery polymers at finite strains. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The elastic response of the network is attributed to the elongation of strands, whereas its plastic behavior is associated with the sliding of nodes with respect to their initial positions. Unlike conventional stress–strain relations in finite viscoplasticity, the rate-of-strain tensor for the sliding of junctions is expressed in terms of the rate-of-strain tensor for macro-deformation. Constitutive equations are developed by using the laws of thermodynamics. These relations are simplified for simple shear of an incompressible medium with finite strains. The governing equations are determined by 3 material constants. To verify the model, a series of shear tests is performed on polycarbonate melts reinforced with short glass fibers. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is shown that the material constants change with the filler content in a physically plausible way.Department of Chemical Engineering, Kuwait University, Safat 13060, Kuwait     

A continuum damage mechanics model with the strain-based approach to biaxial low cycle fatigue failure

A continuum damage mechanics model for low cycle fatigue failure of initially isotropic materials under biaxial loading conditions is presented. The expression for the equivalent strain in the fatigue damage evolution equation contains the three material parameters, and the strain intensity as well as the maximum principal strain and the volume strain for amplitudes. It is shown how these material parameters can be determined from a series of basic experiments using a cruciform specimen. Particular expressions for the equivalent strain with a smaller number of material parameters and invariants are obtained. Model predictions are found to be in satisfactory agreement with the experimental low cycle fatigue data under full ranged biaxial loadings obtained in the test using a cruciform specimen.     

Prediction of constant-amplitude fatigue life to failure under pulsating tension by use of the local-strain approach

The aim of this investigation was to compare local-strain approximation (LSA) life predictions with pulsating-tension tests to failure. It was shown that, in the case of pulsating tension, the ratio N_i/N_f does not change significantly and therefore an LSA calculation can be of use for predicting A-M-N lines for R0. The accuracy of the prediction is associated with the choice of the k-value in Neuber's relation K_σK_ε=k². The -values that give the best life predictions were obtained close to those of the corresponding notch factors for pulsating tension (R=S_min/Smax=0). Because of the size and surface effects (which are not taken into account in LSA), and in view of the difficulty in knowing whether the specimen with a given K_F-value has exactly the same cyclic parameters as those used in the LSA calculations, it is then preferable to use a k-value proved to give prediction results in agreement with some pulsating-tension tests. This k-value may be used for all combinations of S_a and S_m (S_aS_m and S_max<S_y). The results are valid for a specific specimen material, geometry, size and surface finish.     

Review: degradation-induced embrittlement in semi-crystalline polymers having their amorphous phase in rubbery state

The literature dealing with degradation-induced embrittlement mechanisms in semi-crystalline polymers having their amorphous phase in rubbery state is reviewed. It is first demonstrated that the decrease of molar mass resulting from a quasi-homogeneous chain scission process is responsible for embrittlement. The main specificity of the polymer family under study is that embrittlement occurs at a very low conversion of the degradation process, while the entanglement network in the amorphous phase is slightly damaged. In these polymers, chain scission induces chemicrystallization. The analyses of available data on this process show that it is characterized by a relatively high yield: about one half entanglement strands integrate the crystalline phase after one chain scission. A simple relationship expressing the chemicrystallization yield for a given polymer structure is proposed. Chain scission and chemicrystallization can lead to embrittlement through two possible causal chains: (1) chain scission → molar mass decrease → chemicrystallization → decrease of the interlamellar spacing → embrittlement. (2) Chain scission → molar mass decrease → chemicrystallization → decrease of the tie-macromolecule concentration → embrittlement. At this state of our knowledge, both causal chains are almost undistinguishable.     

The effect of temperature on the viscoelastic response of rubbery polymers at finite strains

Summary Constitutive equations are derived for the viscoelastic response of rubbery polymers at finite strains. A polymer is thought of as a network of long chains connected to temporary junctions. At random times, chains detach from the junctions, which is treated as transition from their active state to the dangling state. A dangling chain captures a new junction in the vicinity of its free end at a random instant and returns to its active state. Breakage and reformation of long chains are modeled as thermo-mechanically activated processes. Stress-strain relations for a rubbery polymer are developed using the laws of thermodynamics. Adjustable parameters in the model are found by fitting observations in uniaxial tensile tests for a carbon black filled rubber at various temperatures. Fair agreement is demonstrated between experimental data and results of numerical simulation.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

Static fatigue of thermoplastic elastomers

The failure behaviour in static fatigue of thermoplastic elastomers was estimated on the basis of the stochastic theory proposed for the failure of rubber vulcanizates. A statistical analysis of lifetime distributions for a styrene-butadiene-styrene triblock copolymer (SBS) in creep and stress relaxation experiments was made by using a Weibull distribution, and the failure behaviour of SBS was related to morphological changes of structure in stretched states, observed with a transmission electron microscope. Wear-out failure, in which the failure rate increases with time, occurs in the creep and stress-relaxation processes, and is similar to that in a carbon-reinforced rubber vulcanizate. These results suggest that in SBS, polystyrene (PS) domains dispersed in a continuous polybutadiene matrix serve as physical crosslinks and reinforcing fillers. In the stress relaxation process, however, the increased energy dissipation caused by plastic deformation and disruption of the PS domains leads the material to be more stabilized at a constant stretch ratio. This prolongs the lifetime of the material, due to multi-crack initiation at many portions of a specimen. The differences between the failure behaviour of SBS and that of the rubber vulcanizates are mainly caused by morphological changes of the structure in SBS on deformation.     

Effect of volume fraction of dispersed rubbery phase on the toughness of rubber-toughened epoxy polymers

Journal of Materials Science Letters -