A theory of smeared continuum damage mechanics

This paper considers smeared continuum damage mechanics based on the equivalent elliptical crack representation of a local damage. This approach provides a means of utilizing the crack energies derived in fracture mechanics, and of identifying the local damage state from local stress and strain information. The strain energy equivalence principle is used to derive the effective continuum elastic properties of a damaged solid in terms of the undamaged elastic properties and a scalar damage variable. The scalar damage variable is used to develop a consistent damage evolution equation. The combination of representing local damage as an equivalent elliptical crack, the determination of effective elastic properties using a strain energy equivalence principle, and a consistent damage evolution equation yields a simple, yet powerful local approach for continuum damage analysis     

Shakedown analysis of beams using nonlinear kinematic hardening materials coupled with continuum damage mechanics

The nonlinear kinematic hardening theory of plasticity based on the Armstrong-Fredrick model and isotropic damage was used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. Damage and inelastic deformation were incorporated and they were used for the beam shakedown and ratcheting analysis. The beam material was assumed to follow the nonlinear strain hardening property coupled with isotropic damage. The effect of the damage phenomenon coupled with the elastoplastic nonlinear kinematic hardening was studied for deformation and load control loadings. The Bree's diagram was obtained for two different types of loading, and all numerical results confirmed the reduction of the safe loading domain due to material damage.     

Effect of continuum damage mechanics on springback prediction in metal forming processes

The influence of considering the variations in material properties was investigated through continuum damage mechanics according to the Lemaitre isotropic unified damage law to predict the bending force and springback in V-bending sheet metal forming processes, with emphasis on Finite element (FE) simulation considerations. The material constants of the damage model were calibrated through a uniaxial tensile test with an appropriate and convenient repeating strategy. Holloman’s isotropic and Ziegler’s linear kinematic hardening laws were employed to describe the behavior of a hardening material. To specify the ideal FE conditions for simulating springback, the effect of the various numerical considerations during FE simulation was investigated and compared with the experimental outcome. Results indicate that considering continuum damage mechanics decreased the predicted bending force and improved the accuracy of springback prediction.     

Creep life assessment of aero-engine recuperator based on continuum damage mechanics approach

The creep life of an aeroengine recuperator is investigated in terms of continuum damage mechanics by using finite element simulations. The effects of the manifold wall thickness and creep properties of brazing filler metal on the operating life of the recuperator are analyzed. Results show that the crack initiates from the brazing filler metal located on the outer surface of the manifold with the wall thickness of 2 mm and propagates throughout the whole region of the brazing filler metal when the creep time reaches 34900 h. The creep life of the recuperator meets the requirement of 40000 h continuous operation when the wall thickness increases to 3.5 mm, but its total weight increases by 15%. Decreasing the minimum creep strain rate with the enhancement of the creep strength of the brazing filler metal presents an obvious effect on the creep life of the recuperator. At the same stress level, the creep rupture time of the recuperator is enhanced by 13 times if the mismatch between the minimum creep rate of the filler and base metal is reduced by 20%.     

Theoretical aspects of technological mechanics: 1. Fundamentals of continuum mechanics

Fundamental principles of continuum mechanics are outlined and its basic subdisciplines are identified.     

A continuum mechanics for damaged anisotropic solids

This paper develops a theory of continuum damage mechanics for anisotropic solids on the basis of both the strain energy equivalence principle and the equivalent (fictitious) line crack damage modeling. The strain energy equivalence principle is used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged anisotropic elastic properties and a scalar damage variable. The equivalent line crack representation of local damage provides, a means by which the effective direction of damage propagation can be identified from the local stresses and strains that are available in the course of continuum damage analysis. A scalar damage variable is defined as the effective volume fraction of a damaged zone associated with an equivalent line crack. Finally, an iterative numerical approach to continuum damage analysis is introduced.     

The cell collocation method in continuum mechanics

A new approximate method solution to be called cell collocation, is described. The technique is a special case of the collocation method and consists of taking an approximate function within a region or cell and collocating the governing equations at the centre of the cell.The finite element or boundary element methods generally require numerical evaluation of integrals, over an element. In addition finite elements require assemblying the different matrices into a system matrix. None of these operations are needed in the cell collocation method.     

Non-linear one-dimensional continuum damage theory

The background of Non-Linear Continuum Damage Mechanics is presented for the case of one-dimensional tensile stresses. A brief critical analysis of the existing methods of non-linear damage models construction is given. A new approach to the damage theory development based on the “separability” principle is suggested. The condition of non-linearity and the criterion of long-term failure are formulated. The non-linear damage constitutive equations for static and cyclic loading, allowing one to take into account the loading history, are proposed on this basis. Within the framework of the approach suggested the problems of total and residual lifetime calculation under additional loads and partial unloads are solved. The predictions are compared with experimental data obtained using some particular heat-resistant materials.     

Creep damage evaluation of thick-walled spheres using a long-term creep constitutive model

This paper describes a numerical model developed for the computation of creep damages in a thick-walled sphere subjected to an internal pressure and a thermal gradient. The model predicts the creep damage histories during the life of the sphere, owing to variations in stresses with time and through-thickness variations. The creep damage fraction is based on the Robinson’s linear life fraction damage rule, which has been incorporated in a nonlinear time-dependent stress analysis. Following the stress histories, the effective stress histories are obtained and the creep damages are calculated and summed during the life of the sphere. The material long-term creep properties up to the rupture and creep rupture data are defined by the Θ projection concept [1]. The damage histories up to 38 years are calculated and the results show that the maximum damages are always located at the inner surface of the sphere, while the outer surface of the vessel sustains minimum damages.     

Aero-engine blade fatigue analysis based on nonlinear continuum damage model using neural networks

Fatigue life and reliability of aero-engine blade are always of important significance to flight safety.The establishment of damage model is one of the key factors in blade fatigue research.Conventiona...     

An analysis of localized necking in aluminium alloy tubes during hydroforming using a continuum damage model

In this work, localized necking in aluminium alloy tubes subjected to free hydroforming is analyzed. The main objective is to study the influence of loading conditions, such as prescribed fluid pressure or volume flow rate in conjunction with axial end feed, on the nature of the forming limit curve (FLC). To this end, the strain histories experienced at the tube mid-length, which were computed in an earlier investigation [14] [Varma NSP, Narasimhan R. A numerical study of the effect of loading conditions on tubular hydroforming, Journal of Materials Processing Technology 2005; [Submitted for publication]], are analyzed using the Marciniak–Kuczynski (M–K) method along with an anisotropic version of the Gurson model. The Gurson constitutive parameters are determined following an inverse approach using the sheet FLC for the chosen alloy. The predicted FLC for combined pressure and axial contraction corroborates well with the experimental data obtained in [12] [Kulkarni A, Biswas P, Narasimhan R, Luo A, Stoughton T, Mishra R, Sachdev AK. An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming. International Journal of Mechanical Sciences 46:2004;1727–46] and is almost flat, whereas it is akin to the sheet FLC and increases with negative minor strain when fluid volume is specified. The forming limit strains for loading with specified fluid volume are in general higher when compared to those with prescribed fluid pressure. Finally, it is demonstrated that a transition from axial to circumferential necking occurs when high ratios of axial extension to volume flow rate are applied to the tube.     

Incremental damage mechanics of particle or short-fiber reinforced composites including cracking damage

In particle or short-fiber reinforced composites, cracking of the reinforcements is a significant damage mode because the cracked reinforcements lose load carrying capacity. This paper deals with an incremental damage theory of particle or short-fiber reinforced composites. The composite undergoing damage process contains intact and broken reinforcements in a matrix. To describe the load carrying capacity of cracked reinforcement, the average stress of cracked ellipsoidal inhomogeneity in an infinite body as proposed in the previous paper is introduced. An incremental constitutive relation on particle or short-fiber reinforced composites including progressive cracking of the reinforcements is developed based on Eshelby’s (1957) equivalent inclusion method and Mon and Tanaka’s (1973) mean field concept. Influence of the cracking damage on the stress-strain response of composites is demonstrated.     

An anisotropic creep damage model for multiaxial cyclic loading histories

The purpose of this study is the development of an anisotropic creep damage theory within the continuum damage mechanics, applicable to creep-dominated cyclic loading histories. A damage distribution is expressd in rate form as a symmetric tensor of rank necessary to match physically measured damage. A theoretical model which expresses general anisotropic creep damage phenomena with power law cavity growth is proposed. The coupling of damage with a bounding surface cyclic viscoplasticity theory is also accomplished. Comparison with experimental results are made for weakly anisotropically damaging materials, type 304 stainless steel at 593°C. Good correlation of rupture time, secondary creep, and tertiary creep has been obtained for proportional and nonproportional, isothermal, constant isochronous nominal stress loading histories. A modification of the isochronous stress (the set of stress state which have a same rupture time) for compressive hydrostatic stress state has been offered.     

Cohesive and continuum damage models applied to fracture characterization of bonded joints

In this work, two different methods for simulating damage propagation are presented and applied to fracture characterization of bonded joints in pure modes I and II. The cohesive damage model is based on a special developed interface finite element including a linear softening damage process. In the continuum damage model the softening process is performed by including a characteristic length associated with a given Gauss point. The models were applied to the simulation of “double cantilever beam” (DCB) and “end notched flexure” (ENF) tests used to obtain the critical strain release rates in mode I and II of bonded joints. In mode I it was observed, under certain conditions, a good agreement between the results obtained by the two models with the reference value of critical strain energy release rate in mode I (G_Ic), which is an inputted parameter. However, in mode II some discrepancies on the obtained G_IIc values were observed between the two models. These inaccuracies can be explained by the simplifying assumptions inherent to the cohesive model. Better results were achieved considering the crack equivalent concept.     

基于损伤力学的铸造起重机疲劳-蠕变寿命分析

以连续损伤力学(continuum damage mechanics)理论为基础,针对铸造起重机主梁在中温及组合应力状态下的疲劳-蠕变损伤进行了研究。通过对Q235试件的中温疲劳试验,分别对扭转与拉伸状态下的铸造起重机主梁平均应变进行了分析,推导出了中温状态下的铸造起重机主梁在组合应力状态下的疲劳-蠕变损伤交互作用的损伤模型。在此基础上,研究了铸造起重机箱型梁在损伤后的有效截面尺寸分配原则和计算依据。通过Q235试件拉伸与扭转试验,证明该疲劳-蠕变损伤模型与试验数据符合度较高。通过180/50t铸造起重机工程验证,表明该模型具有较好的寿命预测能力。     

Failure prediction for multi-material creep test specimens using a steady-state creep rupture stress

The steady-state stress distributions in single- and multi-material notched and waisted specimens were investigated for practical creep test specimens using material properties obtained for materials from a service-aged CrMoV pipe weldment. The tri-axial stress conditions existing in notched and waisted specimens machined from welded pipes were identified. By using a steady-state effective failure stress, it has been shown that an approximate method, based on steady-state stress, for the prediction of rupture life and failure position can produce reasonably accurate results. The applicability of the approximate method was confirmed by comparing the results obtained using it with those obtained from corresponding creep continuum damage modelling. These results indicate that use of steady-state stress analysis, as an approximate technique, may be useful for assessing creep failure behaviour, for determining the effect of specimen size and for generating material properties for welded components.     

A novel evolutionary algorithm for determining unified creep damage constitutive equations

The determination of material constants within unified creep damage constitutive equations from experimental data can be formulated as a problem of finding the global minimum of a well defined objective function. However, such an objective function is usually complex, non-convex and non-differentiable. It is difficult to be optimised by classical gradient-based methods. In this paper, the difficulties in the optimisation are firstly identified. Two different objective functions are proposed, analysed and compared. Then three evolutionary programming algorithms are introduced to solve the global optimisation problem. The evolutionary algorithms are particularly good at dealing with problems which are complex, multi-modal and non-differentiable. The results of the study shows that the evolutionary algorithms are ideally suited to the problem. Computational results of using the algorithms to determine the material constants in a set of physically based creep damage constitutive equations from experimental data for an aluminium alloy are presented in the paper to show the effectiveness and efficiency of the three evolutionary algorithms.     

Evaluation of creep properties using small punch creep test for modified 9Cr-1Mo steel

Journal of Mechanical Science and Technology - In the pressure vessel of a very-high-temperature reactor (VHTR), creep damage, which has a fatal adverse effect on safe operation, occurs due to...