Bayesian calibration of continuum damage model parameters for an oxide-oxide ceramic matrix composite using inhomogeneous experimental data

Modeling the high-temperature creep behaviors of 7075 and 2124 aluminum alloys by continuum damage mechanics model

Over the range of variables (temperature and stress) normally encountered in service applications, creep behaviors of 9Cr-1Mo steel were investigated with various models, such as Wilshire model, combination of exponential form and omega (CEO) model, and continuum damage mechanics (CDM) model. First, a series of short-term creep data was prepared to evaluate the material parameters occurring in these models. Then, creep curve, minimum creep rate, and long-term creep life of present 9Cr-1Mo steel were extrapolated with these estimated models. Based on the analysis of obtained results in detail, it suggested that both CDM model and CEO model can give reliable minimum creep rate predictions. However, the most reliable values of long-term creep life are obtained by the CDM model, followed by the Wilshire model and then the CEO model. In particular, the physically based CDM model can provide useful insights into the underlying creep mechanisms. Therefore, the CDM model has promising potential to study the long-term creep behaviors of 9Cr-1Mo steels.

ABSTRACT: The objective of this paper is to develop a two-dimensional Cohesive Element Model (CZM) coupled with a Continuum Damage Mechanics (CDM) model. The novel cohesive element model allows expressing the separation criterion in terms of the damage tensor used in the CDM model implemented in the neighboring volume elements. Above a critical damage value, debonding triggers. The residual tensile and shearing strength of the CZM follow a linear softening law. The proposed model was calibrated against published triaxial compression tests conducted on shale. Single-cohesive zone tests highlight that the proposed approach allows simulation of hardening during damage propagation followed by softening and failure. The model predicts different strengths in tension and compression and different stiffnesses and strengths for different confinements. A boundary-value problem was solved by using a mesh with embedded cohesive zones at all interfaces. It is shown that the 2D model can predict realistic stress/strain curves, stress and strain fields, and fracture patterns for biaxial compression tests. The advantage of the proposed approach is that it can be used to simulate diffuse damage followed by localized fracture with a smooth transfer of field variables between the finite and cohesive elements. 1 INTRODUCTION Simulating fracture propagation from the inception of microscopic cracks to the localization of macroscopic fractures remains a challenge. To date, finite element modeling approaches based on Continuum Damage Mechanics (CDM) and Cohesive Zone Models (CZM) emerge as the most widely used approaches. The goal of this study is to couple both, in order to take advantage of the benefits that each technique can bring. In CDM, sets micro-cracks are represented by a damage tensor, which is modeled as an internal variable within the framework of thermodynamic irreversible processes. Stiffness and strength decrease as damage accumulates. CDM models can be formulated based on phenomenological principles (Xu and Arson, 2014) or micromechanics principles (Jin and Arson, 2017). Exhaustive reviews of damage rock mechanics are available in (Arson and Gatmiri, 2008; Arson, 2020).

A recently developed anisotropic model of continuum damage mechanics has been applied successfully to characterize ductile fracture of cracked plates under mode I and mixed mode failures. The damage model is further extended in this investigation to examine its applicability to include notch ductile fracture of thin plates containing a circular hole. Two hole sizes of 16 mm and 24 mm diameters are chosen and the specimen material is aluminum alloy 2024-T3. Fracture loads of the plates are predicted by the damage model and compared satisfactorily with those determined experimentally. This investigation provides an important confirmation that not only the anisotropic model of continuum damage mechanics but also the same failure criterion developed can be effectively employed to characterize both ductile fracture for plates containing an isolated macro-crack or circular hole which would otherwise not be possible using the conventional theory of fracture mechanics. The successful development of the unified approach to characterize ductile failure provides a vital impetus for design engineers in the general application of the theory of continuum damage mechanics to solve practical engineering problems.

In this paper, the creep‐fatigue responses of the nickel‐based superalloy Inconel 718 have been investigated by conducting hybrid stress–strain‐controlled creep‐fatigue interaction (HCFI) loading experiments at 650°C with different dwell stresses and dwell periods. Deformation responses demonstrate that stress dwell leads to complex cyclic responses, such as an increase in softening rate and changes in inelastic strain rate. Then, a novel creep equivalent stress determination method is proposed based on stress relaxed characteristics. After modifying the continuum damage mechanics (CDM) model with this method, accurate prediction results of the creep‐fatigue cyclic life under strain‐controlled creep‐fatigue loading and HCFI loading can be obtained. Finally, the damage evolutions of Inconel 718 under HCFI loading are analyzed by CDM model. The results of damage evolution indicate that the trend of damage accumulation under different test conditions is consistent with the trend of inelastic strain in the material.

A general stochastic dynamic model of continuum damage mechanics

This paper describes the development of a generalized model of continuum damage mechanics for fatigue fracture. With the introduction of a new damage effect tensor, the necessary constitutive equations of elasticity and plasticity coupled with damage are for the first instance derived. This is followed by the formulations of fatigue damage dissipative potential function and a fatigue damage criterion which are required for the development of a fatigue damage evolution equation. The fatigue evolution model is based on the hypothesis that the overall fatigue damage is induced by the summation of ‘elastic’ and ‘plastic’ damages.

The proposed work addresses the key research need for the development of constitutive models and overall failure models for graphite and high temperature structural materials, with the long-term goal being to maximize the design life of the Next Generation Nuclear Plant (NGNP). To this end, the capability of a Continuum Damage Mechanics (CDM) model, which has been used successfully for modeling fracture of virgin graphite, will be extended as a predictive and design tool for the core components of the very high- temperature reactor (VHTR). Specifically, irradiation and environmental effects pertinent to the VHTR will be incorporated into the model to allow fracture of graphite and ceramic components under in-reactor conditions to be modeled explicitly using the finite element method. The model uses a combined stress-based and fracture mechanics-based failure criterion, so it can simulate both the initiation and propagation of cracks. Modern imaging techniques, such as x-ray computed tomography and digital image correlation, will be used during material testing to help define the baseline material damage parameters. Monte Carlo analysis will be performed to address inherent variations in material properties, the aim being to reduce the arbitrariness and uncertainties associated with the current statistical approach. The results can potentially contribute to the current development of American Society of Mechanical Engineers (ASME) codes for the design and construction of VHTR core components.

This paper develops a 3D homogenization-based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage. Micromechanical damage in the representative volume element (RVE) is explicitly incorporated in the form of fiber—matrix interfacial debonding. The model uses the evolving principal damage coordinate system as its reference in order to represent the anisotropic coefficients. This is necessary for retaining accuracy with nonproportional loading. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as macroscopic internal variable. Damage in 3D composites is accounted for through functional forms of the fourth order damage tensor in terms of macroscopic strain components. The HCDM model parameters are calibrated by using homogenized micromechanical (HMM) solutions for the RVE for a few strain histories. The proposed model is validated by comparing the CDM results with HMM response of single and multiple fiber RVEs subjected to arbitrary loading history. Finally the HCDM model is incorporated in a macroscopic finite element code to conduct damage analysis in a structure. The effect of different microstructures on the macroscopic damage progression is examined through this study.

A temperature-dependent constitutive model based on the continuum damage mechanics (CDM) theory is developed to model the stress/strain behavior of C/SiC composites. A formulation of Helmholtz free energy with initial modulus and tangent modulus is proposed to describe the bilinear constitutive behavior of such materials. The Lagrange interpolation is used to describe the relations between material parameters and temperature. The effect of temperature is introduced into the theoretical framework of continuum damage mechanics. The constitutive model is applied to predict the stress/strain curves of two-dimensional woven C/SiC composite at room and elevated temperatures. Good agreement was found between the experimental data generated and the results predicted by the continuum damage mechanics model. This demonstrates that the methods developed in this paper are effective. The numerical analysis of two-dimensional woven C/SiC laminate with a hole shows that the temperature effect will reduce stress concentration near this hole.

An enhanced continuum damage mechanics model for crash simulation of composites

The interest of this research is to assess the experimental techniques used for ductile damage measurement both in quasistatic and high strain-rate conditions. The results can later be used for the calibration of Continuum Damage Mechanics (CDM) models. A procedure for the evaluation of damage accumulation in quasi-static conditions is presented. The technique used to measure damage is based on the elastic modulus calculation from unloading and reloading cycles performed at different stages of plastic deformation. Tests have been performed in a continuous manner and the strain variations have been recorded using a small gauge extensometer. This methodology includes a second experiment in which the geometry of the specimen is monitored, allowing to extract the true stress-strain behaviour of the material even after necking phenomenon starts. The proposed methodology has been applied to stainless steel 304L. Regarding the high strain-rate conditions, a continuous test cannot be performed due to physical as well as practical difficulties. Therefore, an interrupted methodology has been devised in which the plastic deformation is applied at high strain-rate and the damage measurement is performed separately in quasi-static conditions. An experimental rig has been developed to interrupt high-speed tensile tests at strain-rates up to 103s−1. Its design and preliminary calibration are analysed and its future use for damage assessment discussed.

Thermal and mechanical load induced damage behaviour of a low alloy steel: Mechanisms and modelling

On comparison of creep damage behaviour in two variants of titanium added 14Cr-15Ni stainless steel

To maximize the capabilities of nano- and micro-class satellites, which are limited by their size, weight, and power, advancements in deployable mechanisms with a high deployable surface area to packaging volume ratio are necessary. Without progress in understanding the mechanics of high-strain materials and structures, the development of compact deployable mechanisms for this class of satellites would be difficult. This paper presents fabrication, experimental testing, and progressive failure modeling to study the deformation of an ultra-thin composite beam. The research study examines the deformation modes of a post-deployed boom under repetitive pure bending loads using a four-point bending setup and bending collapse failure under eccentric buckling. The material and fabrication challenges for ultra-thin, high-stiffness (UTHS) composite boom are discussed in detail. The continuum damage mechanics (CDM) model for the beam is calibrated using experimental coupon testing and was used for a finite element explicit analysis of the boom. It is shown that UTHS can sustain a bending radius of 14 mm without significant fiber and matrix damage. The finite element model accurately predicts the localized transverse fiber damage under eccentric buckling and buckling stiffness of 15.6 N/mm. The results of the bending simulation were found to closely match the experimental results, indicating that the simulation accurately shows deformation stages and predicts damage to the material. The findings of this research provide a better understanding of the structure characteristics with the progressive damage model of the UTHS boom, which can be used for designing a complex deployable payload for nano-micro-class satellites.