Linear Damage Accumulation Law Research Articles

Multi-impact behaviour of composite laminates under constant and different energy levels

Composite laminates have been used in the most diverse engineering fields, in which they are often subject to multi-impacts. Typical examples of these phenomena are found in the wind energy industry. However, several studies have focused on this subject, but most involve events with the same energy level. Therefore, this work intends to study the multi-impact behaviour of composite laminates as well as to verify if a linear damage accumulation law can predict the multi-impact life. For this purpose, low-velocity impact tests were carried out with impact energies of 4 J, 6 J, 8 J and 10 J. From the study carried out for single impacts, it was possible to observe that the damaged area increased by around 151.2%, promoting higher impact loads, displacement, and impact bending stiffness for higher impact energy levels, while the restored energy decreased. In terms of multi-impact strength, the classic SN curve was adopted, and the number of impacts to failure varied inversely with the impact energy. Finally, in terms of multi-impact behaviour under different energy levels, the lives resulting from experimental tests and estimated lives based on Palmgren–Miner’s Law did not find a good agreement.

Comparative study on ductile fracture prediction of high-tensile strength marine structural steels

ABSTRACT Accidental events such as collision, grounding, and explosion in marine structures can cause plastic deformation and structural damage. Various fracture models based on different mechanical concepts have been proposed to predict damage extents involving ductile fracture. In this paper, some fracture models were evaluated: Maximum shear stress, Cockcroft-Latham, Johnson-Cook, Modified Mohr-Coulomb, Lou-Huh, and Hosford-Coulomb models. The model parameters were identified for two shipbuilding steel grades: AH36 and DH36. A hybrid experimental-numerical approach was adopted. The parameters of six fracture models were identified using an optimisation algorithm based on the extracted loading paths from the numerical simulations and adopting a linear damage accumulation law. The calibrated fracture models are presented in stress triaxiality and Lode angle parameter space as a 3D fracture locus, and under plain stress condition as a function of the stress triaxiality as a 2D fracture locus. The predictive capabilities and flexibility of the evaluated fracture models were discussed.

Online Evaluation of Turbo-Generator Shaft Fatigue Damage Caused by Subsynchronous Oscillation

Subsynchronous oscillation (SSO) fault can cause torsional vibration and fatigue damage of the shafting system, thereby endanger the safe operation of the turbo-generator set. A novel framework for the online evaluation of shaft fatigue damage suffered from SSO is proposed in this paper. The main ingredients of the framework are a calculation method of the turbo-generator shaft torque, rain-flow counting method, S-N curves and linear damage accumulation law. The shaft torque calculation method, based on the measured torsional angle and generator voltage and current data, is mainly discussed. The effects of damping and electromechanical coupling under complex operating conditions are included in the measured data, and the calculated results of the torque are accurate. The novel framework was used to evaluate the fatigue damage of a 1000 MW turbo-generator shaft that suffered an actual SSO fault caused by a high-voltage direct current (HVDC) transmission system and some meaningful conclusions were given.

Modeling, testing and calibration of ductile crack formation in grade DH36 ship plates

The initiation of ductile fracture in grade DH36 shipbuilding steel was modeled using the Hosford-Coulomb fracture model. The hardening and ductile fracture characteristics of DH36 were assessed by performing experiments on notched tension, central hole tension, plane strain tension and shear specimens. Detailed finite element analysis of each experiment was performed to evaluate the evolution of local stress and strain fields. The loading paths to ductile fracture initiation were determined in terms of the stress triaxiality and Lode angle parameter histories extracted from finite element analyses with very fine solid element meshes. The Hosford-Coulomb fracture model parameters were identified using the extracted loading paths and adopting a linear damage accumulation law. It has been found that ductile fracture behavior of DH36 is dependent not only on the stress triaxiality but also the Lode angle.

Simulation of ship collision and grounding damage using Hosford-Coulomb fracture model for shell elements

The predictive capabilities of the Hosford-Coulomb ductile fracture model for shell elements were evaluated by simulating the penetration of stiffened panel test models. The plasticity and ductile fracture of the test model material, S235JR grade steel, were modeled using the results of tests reported in the literature, which consisted of dog bone, notched tension, central hole tension, and shear experiments. The loading paths to ductile fracture initiation were extracted from finite element analyses with very fine solid element meshes. The Hosford-Coulomb fracture model parameters were identified using the extracted loading paths and adopting a linear damage accumulation law. Using the concept of the Domain of Shell-to-Solid Equivalence, the calibrated fracture model was extended to shell finite elements. Subsequently, the fracture model was used to simulate the stiffened panel penetration tests. The calibrated fracture model provides an accurate estimation of ductile fracture initiation and ductile crack propagation while being relatively mesh-insensitive for the particular problem considered.

PRESSURE- AND LODE-DEPENDENT YIELD CRITERION WITHIN THE PROBLEM OF 2024-T3(51) ALUMINUM ALLOY PLATE PERFORATION BY A RIGID PROJECTILE

The problem of perforation of free circular plates made of 2024-T3(51) aluminum alloy or its Russian analogue D16(A)T with various thicknesses normally impacted at their centers by a rigid spherical projectile is considered. The considered problem is numerically simulated through the finite element method utilizing phenomenological pressure- and Lode-dependent yield and fracture criteria along with an associated flow rule and a linear damage accumulation law to describe the target material deformation and fracture. Comparison of the obtained results with the experimental data as well as with the numerical results calculated using less sophisticated phenomenological material models is made. Necessity of a yield criterion pressure and Lode dependence to provide accuracy of numerical simulation is assessed.

Prediction of Onset of Mode I Delamination Growth Under a Tensile Spectrum Load

In this investigation, the onset of mode I delamination growth under a standard aircraft spectrum load sequence, mini-FALSTAFF truncated to contain only tension-tension fatigue cycles is predicted. The study was carried out on a standard Double Cantilever Beam (DCB) test specimen of Uni Directional (UD) layup Carbon Fiber Composite (CFC) IMA/M21. Finite element modeling and analysis was carried out using ABAQUS standard to determine Strain Energy Release Rate (SERR) by Virtual Crack Closure Technique (VCCT). Both two dimensional (2D) and three dimensional (3D) models were studied. Using the FE analysis results, an empirical equation was derived for SERR (G) and load (P) relationship. Further, the load cycles in the spectrum sequence were rain flow counted to separate individual cycles. For each of the counted cycle, the SERR was obtained and corresponding N onset for that cycle was estimated from the Constant Onset Life Diagram (COLD) of the material. Linear damage accumulation law was used to predict the number of spectrum load blocks required for onset of mode I delamination growth. The prediction was carried out for various reference loads (P ref), and the corresponding reference SERR (G ref) of the spectrum sequence. Predicted results show that decreasing the reference stress increases the mode I delamination onset life under spectrum loads.

ステンレス鋼SUS316Lの低サイクル疲労強度に及ぼす変動振幅ひずみ条件の影響

Low cycle fatigue tests were performed for austenitic stainless steel, JIS SUS316L, used for pressure vessel and piping of engineering plants. This study investigated the effect of variable amplitude strain conditions on the fatigue strength. Fatigue tests were conducted under two-step and repeated two-step variable amplitude strain conditions, in which the influence of straining history on the hardening and softening behavior of the material had an important role on the fatigue strength. The experimental results were compared with predictions of the fatigue lives based on the fracture mechanics approach in conjunction with the hardening and softening behavior. These comparisons were performed for a fatigue usage factor, UF, calculated by the linear damage accumulation law using the fatigue strength diagram obtained under constant amplitude straining tests. The UF value at fracture, UFf, reduced under the variable amplitude straining conditions depending on the straining history. Variations of stress under the strain controlled tests were measured in detail and used for the fatigue life predictions. The results indicate that the minimum value of 0.7 for the UFf gives conservative evaluation of the low-cycle fatigue life.

Ductile fracture prediction in cold forging process chains

The paper presents a new approach for the prediction of ductile fracture occurrence in multi-stage cold forging process chains. The approach combines the fracture criterion proposed by Xue and Wierzbicky with a linear damage accumulation law. Thanks to this feature, the approach is capable of predicting both the location where the failure events occur under the action of external loading and the time they take to be generated. An application to the multi-stage cold forging of a C35 Torx-type socket screw carried out on a double-blow header is presented and results of predictions are compared with experimental observations.

Numerical Simulation of Multiple Cracking in ANSI 304 Stainless Steel Under Thermal Fatigue

We simulate in this article for multiple cracking in ANSI 304 stainless steel under thermal fatigue loading, with the usage of a two-surfaces cyclic plastic model. The fatigue process of multiple cracks is studied, from crack nucleation to crack propagation. The simulation is performed in two steps. First, the crack nucleation is simulated. Monte-Carlo randomization is used to determine the size and the position of surface grains. A modified Jiang’s multiaxial fatigue damage model, in combination with linear damage accumulation law, is used to describe the damage of each grain on the specimen surface. Secondly, the growth behavior of short cracks and long cracks is simulated by using a generalized Paris’ law. The model presented in this study gives predictions in agreement with the experimental data in the depth direction.

Fatigue crack growth in fibre metal laminates under selective variable‐amplitude loading

ABSTRACTTo extend the predictive capability of existing crack growth models for fibre metal laminates under constant amplitude fatigue loading to variable‐amplitude loading, further research on variable‐amplitude fatigue mechanisms in fibre metal laminates is necessary. In response to this need, an experimental study into the effects of multiple overloads, underloads and various block‐loading sequences on crack growth in the fibre metal laminate Glare was investigated. Crack growth retardation effects were observed in the tests; however, the magnitude of these effects was lower than seen in monolithic aluminium because of fibre bridging. As a result, predictions of the observed behaviour were attempted using an existing constant‐amplitude fatigue crack growth model for Glare in combination with a linear damage accumulation law.

Lifetime predictions of polymer matrix composites under constant or monotonic load

A revision of long-term lifetime prediction of composite materials under constant and monotonic load is presented. The main failure criteria revised are energy-based criteria and fracture mechanics. It is shown that they all predict a similar relation between constant stress and constant stress rate failure strength. It is also demonstrated that the methodology proposed by Miyano et al., based on linear damage accumulation law (LCD), produces similar results. Experimental cases published in literature are used to illustrate the theoretical approaches. Finally it is suggested that Monkman–Grant classical equation can be used as a failure criterion for constant strain (or stress) rates. The extrapolation for lower strain rates would permit the long-term strength prediction, based on viscoelastic constitutive law. At last creep strength could be obtained from strength curves by using Miyano et al. methodology.

Reliability analysis for low cycle fatigue life of the aeronautical engine turbine disc structure under random environment

The low cycle fatigue life (LCFL) of the aeronautical engine turbine disc structure is related to the stress–strain level of the disc applied by cyclic load and the life characteristic of the material. The randomness of the basic variables, such as applied load, working temperature, geometrical dimensions and material properties, has significant effect on the statistical properties of the stress and the strain of the disc structure. In most cases, due to the complicated relationship between the LCFL and the basic random variables, it is very difficult to derive the statistical properties of the LCFL analytically, and to analyze the reliability directly. By use of the finite element analysis as a numerical experiment tool, a simulation method is presented to obtain the probability density distributions of the stress level and the strain level at the dangerous points in the turbine disc structure. On the basis of the Linear Damage Accumulation (LDA) law and the simulated probability density distributions of the stress and the strain, two models are presented for the reliability of the LCFL, and the randomness in the life characteristic of the material is taken into consideration in the presented models. The load-life interference and the equivalent probability transformation are developed to construct the third reliability model for the LCFL of the turbine disc as well. The aeronautical engine turbine disc is then introduced to illustrate the feasibility of three reliability models. The calculation results show that the reliability results of models 1 and 2 are in good agreement, which are different from that of model 3. By keeping agreement in the reliability results of three models, we discover an alternative method to identify the damage strength parameter in the LDA law.

Several physicomechanical approaches to the analysis of macroscopic failure. 2. Ductile failure

1. The proposed model of ductile failure is based on the concept of a loss in the load bearing capability of a structural element of the material. It takes into consideration the simultaneous initiation and growth of the pores during plastic deformation. The model allows one to predict the effect of an alternating stress state rigidity, the volume fraction of inclusions, and also their concentration and type on the value of the critical strain during ductile failure. 2. It has been shown that the law of linear damage accumulation gives higher values of the critical strain if the stress state rigidity increases, and lower values if it decreases. The most reliable estimates using the linear damage accumulation law is observed with randomly alternating stress units. Nevertheless, in all of the investigated cases, the error in determining the critical strain ɛf using the linear law did not exceed 17%. In the case where ɛf is only determined by pore growth (nucleation of all of the pores occurs in the earliest stages of plastic deformation), the linear damage accumulation law is followed exactly. 3. Under a mechanism of pore growth caused by structural fragmentation and characteristic of clean materials, the stress state rigidity has less of an effect on the values of ɛf (especially at small values of the rigidity) then during pore nucleation on inclusions which is characteristic of structural materials.

A Uniaxial Damage Accumulation Law for Time-Varying Loading Including Creep-Fatigue Interaction

A differential form for damage accumulation is proposed wherein the rate of damage accumulation is equal to a product of two functions. The first depends only on the present damage and the second has the present value of the controlled quantity (stress or strain) and its time rate as its argument. Such an equation leads to the usual linear damage accumulation law and is incapable of modelling sequence effects. A power function form is proposed and integrated for a trapezoidal waveform with unequal tension and compression holdtimes. Using total strains only this equation can model the separate influences of frequency, holdtime, unequal effects of tension and compression holdtime, as well as mean stress (strain) effects. It includes Coffin’s frequency approach as a special case. The equation is shown to correlate low-cycle fatigue data with holdtime of type 304 stainless steel at 1200°F (649°C) and of cast IN 738 at 1600°F (871°C). It is then used to predict the lifetime for other tests for which no experiments have yet been reported.