continuum damage mechanics

Creep is a time-dependent phenomenon that occurs at high temperatures and leads to the permanent deformation of a material under constant stress. Due to the significance of this phenomenon in high-temperature components, estimating the lifespan of such components has always been challenging. Initially, this estimation was performed using damage-free methods, where the effects of damage, such as crack growth and microstructural defects, were not considered. However, with advances in science and the increasing sensitivity of component performance, damage-based lifespan estimation approaches, such as damage mechanics and fracture mechanics, were introduced. In fracture mechanics, the assumption is the existence of a crack, while in damage mechanics, damage is considered to result from the nucleation of microstructural defects. Therefore, the damage parameter holds particular importance in damage mechanics equations. The evolution of these equations has shown that newer formulations allow for the differentiation of microstructural defects. The limitations of each method have led researchers to gravitate towards combined equations to address these constraints. These equations are primarily based on damage mechanics, highlighting the importance of this approach in lifespan estimation. Despite these advancements, studies related to uncertainty and the performance of components under real-world conditions, which are typically multiaxial, remain limited. It is expected that future research will focus more on these important topics, alongside the development of new relationships based on damage mechanics.

Once a composite laminate is subjected to quasi-static tensile or fatigue loading, some damage modes initiate and propagate in the laminate. The first damage mode is the matrix crack that forms in the layers with an angle to the loading direction. Although not leading to breakage, these cracks reduce the equivalent mechanical properties of the composite laminate. In this paper, a new nonlinear analytical model is presented and used to predict the stiffness degradation of the cross-ply composite laminates. For this purpose, a new third-order polynomial function is proposed as the Helmholtz free energy of the composite, and the appropriate equations are derived. A microscopic experimental test is designed and accompanied by the analytical model to investigate the damage progression in a glass/epoxy cross-ply laminate. Also, finite-element micromechanical models with periodic boundary conditions (PBC) are proposed and used to determine the damage constants. The model is validated against the 3D micromechanical models and the quasi-static uniaxial loading-unloading experimental tests. The validation shows a very good agreement between the model and the experiments.

The theory of continuum damage mechanics with a phenomenological approach is used in predicting the phenomenon of material failure, and since each material has its own behavior, it is especially important to find out the damage behavior of common used metals. In this study, the constants of two damage models, Ganjiani and Bonora, for analyzing the elastoplastic damage behavior of several metals by writing VUMAT subroutine in Abaqus software, simulation and comparison with experimental data in literature, were determined and the ability and efficiency of models in the analysis of metals damage behavior was ensured. In finding the constants of the models, stress-strain, damage-strain and failures train-stress triaxiality diagrams were used and after the simulation, with the help of force-displacement diagram, which had a good agreement with the experimental diagram for each metal, the accuracy of the performance was confirmed. In general, the constants during a trial and error process were determined to be the optimal fit. The studied metals were steel 1045, aluminum 2024-T351and HY130 steel. For the first two metals, only simple tension test is simulated, and for HY130 steel a more general test, three point bending test, is simulated and the obtained force-displacement diagram was compared with the experimental diagram. Also, because the strains were in the range of large strains, the relationships related to large strains have been used.

In this paper, the reliability of rectangular plates without holes and containing a central circular hole under static tensile load has been studied. To investigate the initiation and evolution of damages, continuum damage mechanics approach together with finite element has been used. Constitutive equations with scalar damage have been obtained for the plate and implemented in finite element code, ABAQUS.  To analyze the probability of failure the first/second order reliability methods have been used and then, limit state function and random variables according to the continuum damage mechanics model obtained. The force-displacement curves for various sizes of the hole are obtained. With the addition of a central hole in a plate with a diameter of 2 to 10 mm, failure load is reduced by approximately 60 to 80%, which is consistent with the concepts of stress concentration. Finally, the probability of failure of each plate with different hole sizes is approximated and sensitivity analysis on the coefficient of variation is performed. The reliability of the specimen with a diameter of 10 mm has the lowest value, while the plate without a hole has the highest value and among the random variables, the critical damage is the most effective one in reliability.

The aim of this research is to propose a procedure for predicting creep-fatigue life of gas turbine blade. Components in gas turbine hot section such combustion chamber and turbine gets damaged under effect of thermomechanical loadings. These damages developed via fatigue and creep together, thus it is necessary to identify their interaction on each other. To achieve this goal Chaboche’s elasto-viscoplastic model which is an appropriate model for simulating the behavior of nickel alloys being used. Damage evolution rules for fatigue and creep which introduced by chaboche and kachanov respectively added to viscoplastic model and implemented in Abaqus by a UMAT. After verification of Generated subroutine by a simple model, a rotor blade of last stage of a low pressure turbine was used in the process of creep-fatigue life assessment. Predicted life has proposed in three ways as the operating hours, number of starts and the equivalent operation hours which is the common ways of announcing gas turbines life. Comparison the gained results with common gas turbines life represent that this procedure’s capability and practicality.

 Chopped fiber composites have become attractive materials for many industrial applications due to simplicity of their manufacturing processes and uniform mechanical properties. The subject of this paper is investigation of damage progression in random chopped Eglass fiber/Epoxy composites and evaluation of Chow and Wang Model in simple tensile test. In the experimental section, digital
image correlation method was applied and variation curves of the Young's modulus and Poisson's ratio in tensile test of specimens were extracted until rupture. In theoretical section, for investigation of anisotropic damage and distinguishing between damage mechanism due to tensile and compressive stresses, the first part of the Chow and Wang criterion was employed. Growth of damage variables during the failure progression was characterized and anisotropic damage evolution in this composite was concluded. By means of linear approximation of damage dependency coefficient, validation of the model for prediction of mechanical behavior of the damaged composite was confirmed by comparing with experimental results.

In the current study, semi-crystalline polymers and their properties are introduced, and then a mechanical model is precisely presented in order to predict the behavior of these materials. In this model, a material point of the semi-crystalline polymer is considered as an aggregate of inclusions of two phases, namely, the crystalline and the amorphous phase, with the interface plane of these two phases. Constitutive equations of each phase are demonstrated. A numerical algorithm is presented for solving the constitutive equations of each phase, in stages. Moreover, the general behavior of the material is determined in terms of each phase behavior using volume averaging. Because of the availability of the material parameters for polyethylene, this material has been taken into account. Obtained numerical results are reported and compared to that of previous models. After supporting the validity of the presented model, the effect of some material parameters including crystalline phase damage rate, release parameter, amorphous phase damage rate, saturation damage, rubber shear modulus, and amorphous phase strength on polyethylene behavior has been discussed in details.

In general, materials include micro-cracks and small holes which is created during the manufacturing process. The growth of these micro-cracks leads to degradation of mechanical properties and resulting in deterioration of the materials. Continuum damage mechanics is the new field of failure criteria which survey the behavior and responses of weakened material during the complete process of deterioration of material. This method defines the damage growth with an internal variable and can be used to predict the failure behavior of many materials such as metals, composites, polymers, and so on. Shape memory alloys have unique features, such as, having memorable properties, being super elastic and being energy absorber, which led to new applications in science and engineering research. Super elastic property accompanies with a lot of energy absorption during creating a Hysteresis loop. In this research, we examine mechanical behavior of materials reinforced with smart alloy in the context of environmental damage mechanics. Simulation and experimental results were very close. The considered structure is a notched piece of aluminum which is reinforced by the smart alloy. This material is notched because when the smart alloy reaches to its maximum reversible strain, damage variable reaches to its critical value due to the stress concentration. Accordingly, in this case, the effect of existence of the smart alloy is studied to find how it reduces the growing of the damage. Simulation of the mentioned structure is performed with Finite Element Analysis, where the structure was modeled under longitudinal loading. UMAT code of Lemaiter model, was developed for behavioral properties with damaged aluminum, UMAT code of Brinson model was used for behavioral properties of shape memory alloy. Simulation results suggest that different behavioral aluminum with aluminum reinforced by SMA. Existence of smart alloy on the aluminum substrate reduces the damage evolution and the structure fails in higher loadings. Also, the simulation results showed that reinforcing materials such as aluminum with shape memory alloys, up to the failure, are suitable choices for cyclic loading.

In this article, the isothermal low-cycle fatigue continuum damage in the engine piston aluminum alloy has been evaluated at different temperatures. For this objective, experimental data of low-cycle fatigue tests on standard specimens were used at 280, 350 and 425°C. Based on the continuum damage mechanics method, the fatigue damage was calculated during cyclic loading. Obtained results, including the predicted low-cycle fatigue lifetime of the piston aluminum alloy, indicated that based the maximum value of the relative error and the average error, a proper agreement was achieved, compared to the experimental fatigue lifetime. Applying the continuum damage mechanics approach in each temperature level in a separately condition, reduced significantly the relative error. Then, properties of the engine piston aluminum-silicon alloy based on the continuum damage mechanics model were obtained versus the temperature, under cyclic loadings. Finally, different damage parameter were defined and their results were compared to results of the continuum damage mechanics technique and the superior parameter was defined and selected.

The purpose of this study is to estimate the fatigue life of laminated composites using a novel model based on continuum damage mechanics. For this purpose, a closed form criterion based on the energy method has been presented in the context of damage mechanics such that considers the difference of damage in three directions and moreover is not limited to a special layup. The proposed model has been implemented in the ANSYS finite element software using the material coded by the user (Usermat). The method of characterization of the model constants has been presented in this paper and the constants have been determined for AS4/3501-6 Carbon-Epoxy composite and finally, validation of the model for unidirectional and multidirectional layered composites has been evaluated. For multidirectional laminates, results of fatigue life for cross-ply laminates with hole with the layups [04/904]s and [904/04]s compared with experimental results. The results show that the developed model can predict the fatigue life of laminated composites only by using the material constants which is obtained from experiments of unidirectional laminates in two stress levels.

One of the main advantages for the increasing engineering application of composites in weight-critical structural applications is their high specific stiffness and strength. Composite materials behavior is complicated more than metallic material because of different mechanisms, damage growth rate and effect of them in each other. In this paper, a continuum damage mechanics based model is developed to simulate stiffness degradation and fatigue life prediction of laminated composites under fatigue loading conditions. Damage parameters are used to estimate the degradation of elastic properties in matrix, fiber and shear direction. The material properties of the damage evolution equations are derived by testing on 0° and 90° unidirectional plies and cross-ply laminate. To evaluate the model under multiaxial fatigue loading, arbitrary states of stress and stress ratio available results of experiments on unidirectional 90 , 0 and 30 plies under fatigue loading conditions are used. Also, to evaluate the model for composite laminates with stress concentration results of experiments of pin-loaded cross-ply laminate are used. The obtained results show the capability of proposed model in fatigue life prediction of unidirectional and cross-ply laminates under uniaxial and multiaxial fatigue loading with different states of stress.

This article predicts lifetime of high cycle fatigue loading using Chaboche-Lemaitre damage model. The ChabocheLemaitre damage model takes into account mean stress effect as well as compressive stresses effect, making crack to close. In the this paper, a numerical algorithm is offered to integrate this model implicitly and the obtained algorithm is implemented as a user material subroutine of the ABAQUS finite element software. To reduce computation time, Jump-in-Cycles procedure is used based on fatigue loading simulation. To verify the proposed algorithm, a V-notched specimen is chosen under a fatigue loading with different stress ratios, and its lifetime is compared with experiments. Next, an aviation industry part, main rotor spindle of an aircraft blades, subjected to a variable fatigue loading is analysed.

Continuum Damage Mechanics (CDM) is a powerful tool to solve problems such as large plastic deformation, Where the fracture mechanics is unable to analysis of its effects. Continuum damage mechanics in terms of the internal variable theory of thermodynamics is derived and based on the experimental results on material properties is developed. As regards, Aluminum has an important role in designing and construction of aerospace structures and devices, since its density and strength are suitable to aerospace applications. Al 5083 is one of the most widely used materials in the construction of missiles, space vehicles and sounding rocket structure. In this paper, the continuum damage mechanics principles are studied. Nucleation, development and propagation of damage in Al 5083 are investigated based on Bonora model as a non-linear model. FE simulation of material behavior during failures is carried out by ABAQUS software package and USDFLD subroutine. The results are validated with experimental tests. This comparison shows that the simulation results are agree with that of experimental tests, also the Bonora model can be used of damage modeling of AL 5083.

The aim of this paper is investigation of progressive damage in a metal matrix composite lamina using coupling of micromechanical method and continuum damage mechanics viewpoint. The micromechanical method is a representative volume element based method known simplified unit cell method which possesses the capability of investigating of progressive damage and plastic behavior in the representative volume elements. The studied damage is isotropic and anisotropic based on continuum damage mechanics viewpoint. Under investigation composite system is Carbon/Aluminum composite. The matrix behavior is considered as isotropic and elastoplastic and the fiber behavior is transversely isotropic and elastic. The fiber arrangement within the matrix is regular. The matrix elastoplastic behavior model is included as bi-linear behavior and solution method is successive approximation method. According to available previous studies, Siliconcarbide/Titinium composite system is noticed for validation and comparison with experimental data. Also the effect of fiber volume fraction on the damage progression routine is studied. The results show that by increasing the longitudinal and transverse loadings, the damage variable grows in the fiber direction and perpendicular to the fiber direction and the axial and transverse Young's modulus decrease subsequently. Also the results prove that in longitudinal loading, considering anisotropic damage, damage progression in the fiber direction is more than its growth in perpendicular to the fiber direction. Whereas, under transverse loading, damage growth in perpendicular to the fiber direction is faster.