| Summary: | 博士 === 國立臺灣大學 === 機械工程學研究所 === 90 === This study proposes a micromechanically-based continuum damage mechanics (mCDM) framework which includes the advantages of micro damage mechanics (MDM) and continuum damage mechanics (CDM). By adopting the framework, the damaged constitutive behavior of the homogeneous ductile materials, composite materials and interface are investigated in detail. The constructing procedures of the mCDM can be classed into three steps. Firstly, the physically-based damage internal variables are defined within the microscale. Then, the relations between the damage variables and the damaged material constansts are calculated by adopting homogenization method (HM). Finally, the evolution equations of damage variables and other internal variables are fromulated within the framework of thermodynamics of internal variable (TIV). Having mimimum damage variables and easy to perform are two leading advantages.
In order to exploring the usage of the mCDM models, we first proposed the ductile material mCDM model to characterize the microcavity evolutions of the ductile materials. Other than calculating the damaged stiffness, deriving plastic strain evolution equations, proposing damage evolution equations, formulating loading failure and absolute failure conditions, the model is used to predict the forming limit of the sheet metal forming. After programming the ductile material mCDM into UMAT subroutine of the commercial finite element code ABAQUS, the damage accumumulations of the ball indentation test and the cracked round-bar tensile test are studied.
By combining matrix cracking damage model, fiber rupture damage model, fiber kink band damage model and delamination model, we propsed a complete damage model of the laminated composite materials. The micromechanically-based damage variables of the model are matrix cracking density, fiber rupture volume fraction, fiber kink band volume fraction and delamination rupture strain fraction. The proposed composite damage model can be used to describe the failure and the post-failure behavior of the composite laminates. Moreover, the rupture strength of the off-axis unidirectional laminates subjected to tension and the rupture strength of the 90-degree Iosipescu specimen subjected to shear can be exactly predicted. After programming the composite damage model into UMAT subroutine and UINTER subroutine of the ABAQUS, the stress-strain relations and damage developments of the [0/90] and [0/45/90/-45] laminates, the damage developments of the interface debonding test as well as double cantilever beam fracture test are studied.
Based on the ideas of generalized stress, generalized strain and generalized damage, we propsed a generalized damage constitutive relation. The material damage constitutive relation which describes the damage behavior of the 3D material differential element, the structure damage constitutive relation which describes the damage behavior of the 2D and 1D structural differential elements and the interface damage constitutive relation which describe the damage behavior of the 3D interface defferential element are all the special cases of the generalized damage constitutive relation. After comparing the ductile material mCDM mdoel and contact damage model, we find out the similarity between the material plasticity and the interface frictional slidng, the material damage and the interface wear out. This observation confirms us that plasticity and damage are two foundamental dissipation mechanisms of the nature world.
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