We propose a model based on extreme value statistics(EVS) and combine it with different models for single-asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load...We propose a model based on extreme value statistics(EVS) and combine it with different models for single-asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load and the friction force on a rough interface. We determine that, when the summit distribution is Gumbel and the contact model is Hertzian, we obtain the closest conformity with Amonton’s law. The range over which Gumbel distribution mimics Amonton’s law is wider than that of the Greenwood–Williamson(GW) model. However, exact conformity with Amonton’s law is not observed for any of the well-known EVS distributions. Plastic deformations in the contact area reduce the relative change in pressure slightly with Gumbel distribution. Interestingly, when elasto-plastic contact is assumed for the asperities, together with Gumbel distribution for summits, the best conformity with Amonton’s law is achieved. Other extreme value statistics are also studied, and the results are presented. We combine Gumbel distribution with the GW–McC ool model, which is an improved version of the GW model, and the new model considers a bandwidth for wavelengths α. Comparisons of this model with the original GW–McCool model and other simplified versions of the Bush–Gibson–Thomas theory reveal that Gumbel distribution has a better conformity with Amonton’s law for all values of α. When the adhesive contact model is used, the main observation is that there is some friction for zero or even negative applied load. Asperities with a height even less than the separation between the two surfaces are in contact. For a small value of the adhesion parameter, a better conformity with Amonton’s law is observed. The relative pressure increases for stronger adhesion, which indicates that adhesion-controlled friction is dominated by load-controlled friction. We also observe that adhesion increases on a surface with a lower value of roughness.展开更多
In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was ...In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was investigated using a scanning electron microscope to study the size of the intermetallic compounds from which the pioneer fatigue crack initiated and led to the final failure of the specimen. To determine the maximum size of the intermetallic compounds existing within the cross section of the specimen at higher risk, Gumbel’s extreme-value statistics were utilized. In the present study, the intermetallic compounds contained within the specimen were assumed to be the initial cracks existing in the material before the fatigue tests. A modified linear elastic fracture-mechanics parameter, M, proposed by McEvily et al., was used to analyze the short FCG behavior under different stress ratios, R. The relation between the rate of FCG and M parameter was found to be useful and appropriate for predicting the fatigue lifetimes under different R ratios. Moreover, the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios could be predicted with this method, which utilizes both the FCG law and a statistical distribution of sizes of the most dangerous intermetallic compounds. The evaluated results were in good agreement with the experimental ones. This correspondence indicates that the estimation method proposed in the present study is effective for evaluation of the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios.展开更多
文摘We propose a model based on extreme value statistics(EVS) and combine it with different models for single-asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load and the friction force on a rough interface. We determine that, when the summit distribution is Gumbel and the contact model is Hertzian, we obtain the closest conformity with Amonton’s law. The range over which Gumbel distribution mimics Amonton’s law is wider than that of the Greenwood–Williamson(GW) model. However, exact conformity with Amonton’s law is not observed for any of the well-known EVS distributions. Plastic deformations in the contact area reduce the relative change in pressure slightly with Gumbel distribution. Interestingly, when elasto-plastic contact is assumed for the asperities, together with Gumbel distribution for summits, the best conformity with Amonton’s law is achieved. Other extreme value statistics are also studied, and the results are presented. We combine Gumbel distribution with the GW–McC ool model, which is an improved version of the GW model, and the new model considers a bandwidth for wavelengths α. Comparisons of this model with the original GW–McCool model and other simplified versions of the Bush–Gibson–Thomas theory reveal that Gumbel distribution has a better conformity with Amonton’s law for all values of α. When the adhesive contact model is used, the main observation is that there is some friction for zero or even negative applied load. Asperities with a height even less than the separation between the two surfaces are in contact. For a small value of the adhesion parameter, a better conformity with Amonton’s law is observed. The relative pressure increases for stronger adhesion, which indicates that adhesion-controlled friction is dominated by load-controlled friction. We also observe that adhesion increases on a surface with a lower value of roughness.
文摘In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was investigated using a scanning electron microscope to study the size of the intermetallic compounds from which the pioneer fatigue crack initiated and led to the final failure of the specimen. To determine the maximum size of the intermetallic compounds existing within the cross section of the specimen at higher risk, Gumbel’s extreme-value statistics were utilized. In the present study, the intermetallic compounds contained within the specimen were assumed to be the initial cracks existing in the material before the fatigue tests. A modified linear elastic fracture-mechanics parameter, M, proposed by McEvily et al., was used to analyze the short FCG behavior under different stress ratios, R. The relation between the rate of FCG and M parameter was found to be useful and appropriate for predicting the fatigue lifetimes under different R ratios. Moreover, the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios could be predicted with this method, which utilizes both the FCG law and a statistical distribution of sizes of the most dangerous intermetallic compounds. The evaluated results were in good agreement with the experimental ones. This correspondence indicates that the estimation method proposed in the present study is effective for evaluation of the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios.