A Mathematical Model for Internal Friction and Local Fatigue Damage Based on Populations of Yielding Microelements

1987 ◽  
Vol 109 (2) ◽  
pp. 201-206 ◽  
Author(s):  
P. W. Whaley
Keyword(s):  
Mathematical Model ◽  
Internal Friction ◽  
Fatigue Damage ◽  
Strain Energy ◽  
Crack Nucleation ◽  
Second Law Of Thermodynamics ◽  
Microplastic Deformation ◽  
Irreversible Processes ◽  
Amplitude Dependence ◽  
Microplastic Strain

A mathematical model for internal friction and fatigue damage based on populations of yielding microelements is described. Using two parameters, the model accounts for amplitude dependence of material damping. For low excitation levels the Zener theory of thermoelasticity is reproduced. The significance of this new damping model is that fatigue damage due to local accumulations of microplastic deformation is quantified. The entropy production is defined by expressing the second law of thermodynamics for irreversible processes as an equality, and quantifying local accumulations of microplastic strain energy as the source of irreversibility. A critical entropy threshold is defined in terms of the local microplastic strain energy density of local failure. The hypothesis is offered that local fatigue damage leading to crack nucleation occurs by exceeding the critical entropy threshold.

Strain Amplitude Dependence of Damping Capacity in High Damping Mg-Based Alloys Continuously Extending to Microplastic Strain

2010 ◽  
Vol 97-101 ◽  
pp. 937-940
Author(s):  
Di Qing Wan ◽  
Bo Lin He ◽  
Jin Cheng Wang ◽  
Gen Cang Yang
Keyword(s):  
Strain Amplitude ◽  
Low Frequency ◽  
Microplastic Deformation ◽  
Damping Capacity ◽  
Amplitude Dependence ◽  
Two Stage ◽  
Microplastic Strain ◽  
Damping Behavior ◽  
Dependent Part ◽  
Weakly Dependent

An investigation on low frequency strain amplitude dependence damping characteristic of as-cast high damping Mg-based alloys continuously extending to microplastic strain was carried out. Two-stage damping behavior via strain amplitude was particularly reported. The first is the strain amplitude strongly dependent part due to breakaway loss and the second is the strain amplitude weakly dependent part due to microplastic deformation loss, which is also frequency dependent. The damping mechanism is discussed in detail.

Nonlinear Dynamics of an Oilless Reciprocating Compressor

1993 ◽  
Author(s):  
Constantinos Minas
Keyword(s):  
Mathematical Model ◽  
Mechanical System ◽  
Input Voltage ◽  
Amplitude Dependence ◽  
Integration Step ◽  
Damped System ◽  
Steady State Operation ◽  
Pressure Term ◽  
Sinusoidal Input ◽  
Mass Flow Rates

Abstract Two modeling methodologies of the dynamics of a motor-compressor system are presented. The first approach considered only the mechanical system subjected to a sinusoidal input force with the pressure term in the equation of motion treated as a nonlinear stiffness term. The second methodology consisted of a mathematical model that couples the electromagnetic and thermodynamic equations to the dynamic equations that describe the motion of the piston. The mathematical model which consisted of a set of four first order simultaneous nonlinear time varying differential equations, was solved by numerical integration routines that use the Adams-Moulton method with an adaptive integration step. The two methodologies are illustrated through an example. Steady-state operation was shown to be reached rapidly after a 0.13s transient. An analysis at various amplitudes and frequencies of the input voltage in the driver-coil of the motor, showed the amplitude dependence of the resonant frequency of the mechanical system, and a heavily damped system when operating at the design amplitude. The most efficient frequency of operation was also determined for a variety of required mass flow rates.

High Cycle Fatigue Damage Evaluation of Steel Pipelines Based on Microhardness Changes During Cyclic Loads: Part II

2018 ◽  
Author(s):  
Geovana Drumond ◽  
Bianca Pinheiro ◽  
Ilson Pasqualino ◽  
Francine Roudet ◽  
Didier Chicot
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
High Cycle Fatigue ◽  
Steel Structures ◽  
New Method ◽  
Microplastic Deformation ◽  
Surface Phenomenon ◽  
Cyclic Loads ◽  
Cycle Fatigue ◽  
Indentation Tests

The hardness of a material shows its ability to resist to microplastic deformation caused by indentation or penetration and is closely related to the plastic slip capacity of the material. Therefore, it could be significant to study the resistance to microplastic deformations based on microhardness changes on the surface, and the associated accumulation of fatigue damage. The present work is part of a research study being carried out with the aim of proposing a new method based on microstructural changes, represented by a fatigue damage indicator, to predict fatigue life of steel structures submitted to cyclic loads, before macroscopic cracking. Here, Berkovich indentation tests were carried out in the samples previously submitted to high cycle fatigue (HCF) tests. It was observed that the major changes in the microhardness values occurred at the surface of the material below 3 μm of indentation depth, and around 20% of the fatigue life of the material, proving that microcracking is a surface phenomenon. So, the results obtained for the surface of the specimen and at the beginning of the fatigue life of the material will be considered in the proposal of a new method to estimate the fatigue life of metal structures.

scholarly journals Strain energy-based rubber fatigue life prediction under the influence of temperature

2018 ◽  
Vol 5 (10) ◽  
pp. 180951 ◽  
Author(s):  
Jingnan Zhang ◽  
Fengxian Xue ◽  
Yue Wang ◽  
Xin Zhang ◽  
Shanling Han
Keyword(s):  
Fatigue Life ◽  
Prediction Model ◽  
Fatigue Damage ◽  
Strain Energy ◽  
Life Prediction ◽  
Least Square ◽  
Fatigue Life Prediction ◽  
Uniaxial Tensile ◽  
Influence Of Temperature ◽  
Different Temperatures

Aiming at the problem of the fatigue life prediction of rubber under the influence of temperature, the effects of thermal ageing and fatigue damage on the fatigue life of rubber under the influence of temperature are analysed and a fatigue life prediction model is established by selecting strain energy as a fatigue damage parameter based on the uniaxial tensile data of dumbbell rubber specimens at different temperatures. Firstly, the strain energy of rubber specimens at different temperatures is obtained by the Yeoh model, and the relationship between it and rubber fatigue life at different temperatures is fitted by the least-square method. Secondly, the function formula of temperature and model parameters is obtained by the least-square polynomial fitting. Finally, another group of rubber specimens is tested at different temperatures and the fatigue characteristics are predicted by using the proposed prediction model under the influence of temperature, and the results are compared with the measured results. The results show that the predicted value of the model is consistent with the measured value and the average relative error is less than 22.26%, which indicates that the model can predict the fatigue life of this kind of rubber specimen at different temperatures. What's more, the model proposed in this study has a high practical value in engineering practice of rubber fatigue life prediction at different temperatures.

Amplitude dependence of the internal friction of Cu-Mn-Al alloys with a martensite transformation

1991 ◽  
Vol 33 (3) ◽  
pp. 235-238 ◽  
Author(s):  
V. A. Evsyukov ◽  
V. M. Kopylova ◽  
N. V. Agapitova ◽  
M. N. Garshina ◽  
L. V. Nikiforova
Keyword(s):  
Internal Friction ◽  
Martensite Transformation ◽  
Al Alloys ◽  
Amplitude Dependence

Thermodynamics as a fundamental science of reliability

2016 ◽  
Vol 230 (6) ◽  
pp. 598-608 ◽  
Author(s):  
Anahita Imanian ◽  
Mohammad Modarres
Keyword(s):  
Energy Dissipation ◽  
Entropy Generation ◽  
Damage Model ◽  
Second Law Of Thermodynamics ◽  
Reliability Function ◽  
Cumulative Damage ◽  
Life Assessment ◽  
Irreversible Processes ◽  
Second Law ◽  
Cumulative Hazard

Cumulative hazard and cumulative damage are important models for reliability and structural integrity assessment. This article reviews a previously developed thermodynamic entropy–based damage model and derives and demonstrates an equivalent reliability function. As such, a thermodynamically inspired approach to developing new definitions of cumulative hazard, cumulative damage, and life models of structures and components based on the second law of thermodynamics is presented. The article defines a new unified measure of damage in terms of energy dissipation associated with multiple interacting irreversible processes that represent the underlying failure mechanisms that cause damage and failure. Since energy dissipation leads to entropy generation in materials, it has been shown and experimentally demonstrated that the use of the total entropy generated in any degradation process is measurable and can ultimately be used to represent the time of failure of structures and components. This description therefore connects the second law of thermodynamics to the conventional models of reliability used in life assessment. Any variability in the entropic endurance to failure and uncertainties about the parameters of the entropic-based damage model lead to the time-to-failure distribution. In comparison with the conventional probabilistic reliability methods, deriving the reliability function in terms of the entropy generation can offer a general and more fundamental approach to representation of reliability. The entropic-based theory of damage and the equivalent reliability approach are demonstrated and confirmed experimentally by applying the complex interactive corrosion-fatigue degradation mechanism to samples of aluminum materials.

Nonlinear Cumulative Fatigue Damage Model

2011 ◽  
Vol 328-330 ◽  
pp. 1440-1444
Author(s):  
Hua Zou ◽  
Qiang Li ◽  
Shou Guang Sun
Keyword(s):  
Mathematical Model ◽  
Aluminum Alloy ◽  
Fatigue Life ◽  
Fatigue Damage ◽  
Welded Joint ◽  
Damage Model ◽  
Reasonable Explanation ◽  
Curve Method ◽  
Cumulative Fatigue Damage ◽  
Damage Rule

Cumulative fatigue damage is an important consideration in determining the fatigue life of structures. A cumulative linear damage rule cannot provide a reasonable explanation for cumulative fatigue damage, but a damage curve method based on nonlinear cumulative fatigue damage model can give a reasonable explanation. In this paper, a specific mathematical model is put forward, which is based on the damage curve method. In the model, miner formula is modified properly and an exponent formula is give out to fit the damage accumulate. According to a two-step fatigue test of aluminum–alloy welded joint, the comparison between the calculated results and the testing results is less than 5%. It shows that the model is reasonable and accuracy.

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