Excellent Wear Resistance of a High-Speed Train Brake Disc Steel with High Hardening Ratcheting Strain Zone

Wear resistance of brake discs has a significant effect on the safety of high-speed trains. In this work, the rolling–sliding wear resistance of a low-carbon martensitic brake disc steel was investigated. The microstructure evolution and mechanical properties from the worn surface to the matrix were analyzed to promote parameters for the application of this steel. The results indicated that a ratcheting strain zone was formed at the surface of the brake disc steel under asymmetric cycling load and presented the morphology of the plastic flow line. An equation between the shear strain and the depth from the surface was established, which reflected the gradient distribution of the shear strain. The martensite lath refined into the nano/sub-micron grain and strip on the topmost surface. The micron scratch test results exhibited that the hardening rate and fracture toughness of the ratcheting strain zone varied continually along with depth, and the highest hardening rate occurred on the worn surface due to the increase of dislocation density and grain refinement. Additionally, the brake disc steel obtained better wear resistance than that of other wear-resistant materials used for railways due to steel having the highest hardening rate in the ratcheting strain zone.

Ratcheting response of biological tissues over asymmetric loading cycles

The purpose of this study is to examine the ratcheting phenomenon in a variety of biological tissues including the trabecular bone, meniscus, articular cartilage and skin, and propose a parametric model to predict the ratcheting strain of these tissues. Furthermore, utilizing experimental data, and the influence of different mechanical and biological parameters on the ratcheting strain are discussed. The dependency of ratcheting on frequency, stress rate, stress variation, physiological environment, and tissue sites is demonstrated. Besides, stiffness of the toe and linear regions in each cycle, and the modulus of the failure region of the stress-strain curve are computed. The energy dissipation in different cycles at two frequencies of 1 Hz and 10 Hz is discussed. A parametric model was employed to predict ratcheting behavior of the said biological tissues. The model predictions of the strain accumulation in tissues are found in agreement with the experimental data.

Ratcheting response of biological tissues over asymmetric loading cycles

The purpose of this study is to examine the ratcheting phenomenon in a variety of biological tissues including the trabecular bone, meniscus, articular cartilage and skin, and propose a parametric model to predict the ratcheting strain of these tissues. Furthermore, utilizing experimental data, and the influence of different mechanical and biological parameters on the ratcheting strain are discussed. The dependency of ratcheting on frequency, stress rate, stress variation, physiological environment, and tissue sites is demonstrated. Besides, stiffness of the toe and linear regions in each cycle, and the modulus of the failure region of the stress-strain curve are computed. The energy dissipation in different cycles at two frequencies of 1 Hz and 10 Hz is discussed. A parametric model was employed to predict ratcheting behavior of the said biological tissues. The model predictions of the strain accumulation in tissues are found in agreement with the experimental data.

Modifications on A-F Hardening Rule to Assess Ratcheting Response of Materials and Its Interaction with Fatigue Damage under Uniaxial Stress Cycles

Ratcheting deformation is accumulated progressively over three distinct stages in materials undergoing asymmetrical cyclic stresses. The present thesis evaluates the triphasic ratcheting response of materials from two stand points: (i) Mechanistic approach at which stages of ratcheting progress over stress cycles was related to mechanistic parameters such as stress level, lifespan, mechanical properties and the softening/hardening response of materials. Mechanistic approach formulated in this thesis was employed to assess ratcheting strain over triphasic stages in various steel and copper alloys under uniaxial stress cycles. Good agreements were achieved between the predicted ratcheting strain values based on the proposed formulation and those of experimentally reported. (ii) Kinematic hardening rule approach at which the hardening rule was characterized by the yield surface translation mechanism and the corresponding plastic modulus calculated based on the consistency condition. Various cyclic plasticity models were employed to assess ratcheting response of materials under different loading conditions. The Armstrong-Frederick (A-F) hardening rule was taken as the backbone of ratcheting analysis developed in this thesis mainly due to less complexity and number of coefficients in the hardening rule as compared with other earlier developed hardening rules in the literature. To predict triphasic ratcheting strain over stress cycles, the A-F hardening rule has been further developed by means of new strain rate coefficients γ2 and δ. These coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting over its progressive stages. The modified hardening formulation holds the coefficients of the hardening rule to control stress-strain hysteresis loops generated over stress cycles during ratcheting process plus the ratcheting rates over stages I, II, and III. These coefficients were calibrated and defined based on the applied stress levels. The constructed calibration curves were employed to determine strain rate coefficients required to assess ratcheting response of materials under uniaxial loading conditions at various cyclic stress levels. The predicted ratcheting strain values based on the modified hardening rule were found in good agreements with the experimentally obtained ratcheting data over stages I and II under uniaxial loading conditions. The capability of the modified hardening rule to assess ratcheting deformation of materials under multi-step uniaxial loading spectra was also assessed. Subsequent load steps were considerably affected by previous load steps in multi-step loading conditions. Ratcheting strains for low-high stress steps were successfully predicted by the modified hardening rule. High-low loading sequences however resulted in an overestimated reversed ratcheting strain in the later load steps. The modified hardening rule proposed in this thesis was then employed to predict the ratcheting strain and its concurrent interaction with fatigue damage over stress cycles in steel alloys. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude, and cyclic softening/hardening response of materials. The extent of ratcheting effect on the overall damage of steel samples was defined by means of the product of the average ratcheting strain rate over the stress cycles and the applied maximum cyclic stress, while fatigue damage was analysed based on earlier developed energy-based models of Xia-Ellyin and Smith-Watson-Topper. Overall damage induced by both ratcheting and fatigue was calibrated through a weighting factor at various ratios of mean stress/cyclic amplitude stress. The estimated lives based on the proposed algorithm at different mean stresses and stress amplitudes showed good agreements as compared with experiments.

Modifications on A-F Hardening Rule to Assess Ratcheting Response of Materials and Its Interaction with Fatigue Damage under Uniaxial Stress Cycles

Ratcheting deformation is accumulated progressively over three distinct stages in materials undergoing asymmetrical cyclic stresses. The present thesis evaluates the triphasic ratcheting response of materials from two stand points: (i) Mechanistic approach at which stages of ratcheting progress over stress cycles was related to mechanistic parameters such as stress level, lifespan, mechanical properties and the softening/hardening response of materials. Mechanistic approach formulated in this thesis was employed to assess ratcheting strain over triphasic stages in various steel and copper alloys under uniaxial stress cycles. Good agreements were achieved between the predicted ratcheting strain values based on the proposed formulation and those of experimentally reported. (ii) Kinematic hardening rule approach at which the hardening rule was characterized by the yield surface translation mechanism and the corresponding plastic modulus calculated based on the consistency condition. Various cyclic plasticity models were employed to assess ratcheting response of materials under different loading conditions. The Armstrong-Frederick (A-F) hardening rule was taken as the backbone of ratcheting analysis developed in this thesis mainly due to less complexity and number of coefficients in the hardening rule as compared with other earlier developed hardening rules in the literature. To predict triphasic ratcheting strain over stress cycles, the A-F hardening rule has been further developed by means of new strain rate coefficients γ2 and δ. These coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting over its progressive stages. The modified hardening formulation holds the coefficients of the hardening rule to control stress-strain hysteresis loops generated over stress cycles during ratcheting process plus the ratcheting rates over stages I, II, and III. These coefficients were calibrated and defined based on the applied stress levels. The constructed calibration curves were employed to determine strain rate coefficients required to assess ratcheting response of materials under uniaxial loading conditions at various cyclic stress levels. The predicted ratcheting strain values based on the modified hardening rule were found in good agreements with the experimentally obtained ratcheting data over stages I and II under uniaxial loading conditions. The capability of the modified hardening rule to assess ratcheting deformation of materials under multi-step uniaxial loading spectra was also assessed. Subsequent load steps were considerably affected by previous load steps in multi-step loading conditions. Ratcheting strains for low-high stress steps were successfully predicted by the modified hardening rule. High-low loading sequences however resulted in an overestimated reversed ratcheting strain in the later load steps. The modified hardening rule proposed in this thesis was then employed to predict the ratcheting strain and its concurrent interaction with fatigue damage over stress cycles in steel alloys. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude, and cyclic softening/hardening response of materials. The extent of ratcheting effect on the overall damage of steel samples was defined by means of the product of the average ratcheting strain rate over the stress cycles and the applied maximum cyclic stress, while fatigue damage was analysed based on earlier developed energy-based models of Xia-Ellyin and Smith-Watson-Topper. Overall damage induced by both ratcheting and fatigue was calibrated through a weighting factor at various ratios of mean stress/cyclic amplitude stress. The estimated lives based on the proposed algorithm at different mean stresses and stress amplitudes showed good agreements as compared with experiments.

The influence of stress level on the ratcheting magnitude and progress rate in steel alloys under uniaxial loading conditions

Engineering materials in their service life undergo symmetric or asymmetric fatigue loading, which leads to fatigue damage in the material. Ratcheting damage is due to the application of mean stress under cyclic loading condition. From deformation behavior perspective, application of mean stress under stress-controlled fatigue loading gives rise to accumulation of plastic strain in the material. Ratcheting strain increases with an increase in applied mean stress and stress amplitude. In addition, ratcheting behavior will increase in cyclic damage with the rise in strain accumulation and it can be illustrated by a shift in the hysteresis loop towards large plastic strain amplitudes. This study focuses on the ratcheting behavior of different steel materials under uniaxial cyclic loading condition and suggests a suitable method to arrest ratcheting by loading the materials at zero ratcheting strain rate condition with specified mean stress and stress amplitudes. The three dimensional surface is created with stress amplitude, mean stress and ratcheting strain rate for different steel materials. This represents a graphical surface zone to study the ratcheting strain rates for various mean stress and stress amplitude combinations.

Development of a kinematic hardening rule to assess ratcheting response of materials under various multiaxial loading spectra

The present thesis develops an Armstrong-Frederick (A-F) type coupled kinematic hardening rule to assess ratcheting response of steel alloys under various multiaxial loading paths. The hardening rule is constructed on the basis of the recently proposed Ahmadzadeh-Varvani (AV) hardening rule to further evaluate the ratcheting response of materials under multiaxial loading spectra. The modified model offers a simple framework with limited number of terms and coefficients in the dynamic recovery portion of the model. The dynamic recovery further holds inner product of plastic strain increment p dand backstress unit vector a a with different directions under multiaxial stress cycles enables the model to track different directions. Term 1/ 2 n. a a taking positive values less than unity for multiaxial loading conditions is to control the accumulation rate of ratcheting strain and to prevent the modified model to experience plastic shakedown over stress cycles in stage II. Term(2 n. a a ) taking the values between 1 and 3 under multiaxial loading, magnifies the effect of coefficient γ2 to take into account the nonproportionality effect of various loading paths and further to shift down the predicted ratcheting strain over the stress cycles. The predicted ratcheting curves by the modified rule were compared with those predicted based on earlier developed hardening rules of Ohno-Wang (O-W), Jiang-Sehitoglu (J-S), McDowell, and Chen-Jiao-Kim (C-J-K) holding relatively complex framework and more number of coefficients. The O-W, the J-S, McDowell and C-J-K models mainly deviated from the experimental ratcheting strain of steel alloys for various multiaxial loading histories, while the predicted curves of the modified model closely agreed with experimental data of steel samples over ratcheting stages. The predicted ratcheting curves based on the modified model closely agreed with experimental data of steel samples under various multiaxial step-loading histories. The modified model was also found capable of predicting ratcheting in the opposite direction as the tensile axial mean stress dropped in magnitude. The O-W, J-S, McDowell and C-J-K models holding more backstress components and coefficients require longer Central Processing Unit (CPU) time. While time required for ratcheting assessment using the modified hardening rule was found to be twice shorter due to its simpler framework and limited number of coefficients.

The influence of stress level on the ratcheting magnitude and progress rate in steel alloys under uniaxial loading conditions

Engineering materials in their service life undergo symmetric or asymmetric fatigue loading, which leads to fatigue damage in the material. Ratcheting damage is due to the application of mean stress under cyclic loading condition. From deformation behavior perspective, application of mean stress under stress-controlled fatigue loading gives rise to accumulation of plastic strain in the material. Ratcheting strain increases with an increase in applied mean stress and stress amplitude. In addition, ratcheting behavior will increase in cyclic damage with the rise in strain accumulation and it can be illustrated by a shift in the hysteresis loop towards large plastic strain amplitudes. This study focuses on the ratcheting behavior of different steel materials under uniaxial cyclic loading condition and suggests a suitable method to arrest ratcheting by loading the materials at zero ratcheting strain rate condition with specified mean stress and stress amplitudes. The three dimensional surface is created with stress amplitude, mean stress and ratcheting strain rate for different steel materials. This represents a graphical surface zone to study the ratcheting strain rates for various mean stress and stress amplitude combinations.

Development of a kinematic hardening rule to assess ratcheting response of materials under various multiaxial loading spectra

The present thesis develops an Armstrong-Frederick (A-F) type coupled kinematic hardening rule to assess ratcheting response of steel alloys under various multiaxial loading paths. The hardening rule is constructed on the basis of the recently proposed Ahmadzadeh-Varvani (AV) hardening rule to further evaluate the ratcheting response of materials under multiaxial loading spectra. The modified model offers a simple framework with limited number of terms and coefficients in the dynamic recovery portion of the model. The dynamic recovery further holds inner product of plastic strain increment p dand backstress unit vector a a with different directions under multiaxial stress cycles enables the model to track different directions. Term 1/ 2 n. a a taking positive values less than unity for multiaxial loading conditions is to control the accumulation rate of ratcheting strain and to prevent the modified model to experience plastic shakedown over stress cycles in stage II. Term(2 n. a a ) taking the values between 1 and 3 under multiaxial loading, magnifies the effect of coefficient γ2 to take into account the nonproportionality effect of various loading paths and further to shift down the predicted ratcheting strain over the stress cycles. The predicted ratcheting curves by the modified rule were compared with those predicted based on earlier developed hardening rules of Ohno-Wang (O-W), Jiang-Sehitoglu (J-S), McDowell, and Chen-Jiao-Kim (C-J-K) holding relatively complex framework and more number of coefficients. The O-W, the J-S, McDowell and C-J-K models mainly deviated from the experimental ratcheting strain of steel alloys for various multiaxial loading histories, while the predicted curves of the modified model closely agreed with experimental data of steel samples over ratcheting stages. The predicted ratcheting curves based on the modified model closely agreed with experimental data of steel samples under various multiaxial step-loading histories. The modified model was also found capable of predicting ratcheting in the opposite direction as the tensile axial mean stress dropped in magnitude. The O-W, J-S, McDowell and C-J-K models holding more backstress components and coefficients require longer Central Processing Unit (CPU) time. While time required for ratcheting assessment using the modified hardening rule was found to be twice shorter due to its simpler framework and limited number of coefficients.