Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part II: Failure Mechanisms

1997 ◽  
Vol 64 (4) ◽  
pp. 763-771 ◽  
Author(s):  
M. W. Schraad ◽  
N. Triantafyllidis
Keyword(s):  
Failure Modes ◽  
Scale Effects ◽  
Unit Cell ◽  
Equilibrium Path ◽  
Planar Lattice ◽  
Loss Of Ellipticity ◽  
Finite Models ◽  
Load Paths ◽  
Periodic Microstructures ◽  
Strain Space

Using the nonlinearly elastic planar lattice model presented in Part I, the influence of scale (i.e., the size of the representative volume, relative to the size of the unit cell) on the onset of failure in periodic and nearly periodic media is investigated. For this study, the concept of a microfailure surface is introduced—this surface being defined as the locus of first instability points found along radial load paths through macroscopic strain space. The influence of specimen size and microstructural imperfections (both geometric and constitutive) on these failure surfaces is investigated. The microfailure surface determined for the infinite model with perfectly periodic microstructure, is found to be a lower bound for the failure surfaces of perfectly periodic, finite models, and an upper bound for the failure surfaces of finite models with microstructural imperfections. The concept of a macrofailure surface is also introduced—this surface being defined as the locus of points corresponding to the loss of ellipticity in the macroscopic (homogenized) moduli of the model. The macrofailure surface is easier to construct than the microfailure surface, because it only requires calculation of the macroscopic properties for the unit cell, at each loading state along the principal equilibrium path. The relation between these two failure surfaces is explored in detail, with attention focused on their regions of coincidence, which are of particular interest due to the possible development of macroscopically localized failure modes.

Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part I: Macroscopic Properties

1997 ◽  
Vol 64 (4) ◽  
pp. 751-762 ◽  
Author(s):  
M. W. Schraad ◽  
N. Triantafyllidis
Keyword(s):  
Heterogeneous Media ◽  
Scale Effects ◽  
Relative Size ◽  
Macroscopic Strain ◽  
Planar Lattice ◽  
Analytical Approximations ◽  
Macroscopic Properties ◽  
Periodic Microstructures ◽  
The Difference ◽  
Nonlinearly Elastic

Traditional averaging and homogenization techniques, developed to predict the macroscopic properties of heterogeneous media, typically ignore microstructure related scale effects—that is, the influence of the size of the representative volume, relative to the size of the unit cell. This issue is presently investigated by exploring the behavior of a nonlinearly elastic, planar, lattice model, which is subjected to general macroscopic deformations. For these materials, scale effects may be due to nonuniformities in the macroscopic strain field throughout the specimen, or alternatively, to the presence of microstructural imperfections that may be either geometric or constitutive in nature. For the case of macroscopic strain nonuniformities, it is shown that the microstructure related scale effects can be accounted for by the presence of higher order gradient terms in the macroscopic strain energy density of the model. For the case of microstructural imperfections, the difference between the respective macroscopic properties of the perfect and imperfect models are shown to depend on the relative size of the specimen, and on the imperfection amplitude and wavelength, while being nearly insensitive to the imposed macroscopic strain. For all of the cases considered, several analytical approximations are proposed to predict the influence of scale on the macroscopic properties, and the accuracy of each method is examined.

Study on shear performance of the connection with external stiffening ring between square steel tubular column and unequal-depth steel beams

2020 ◽  
pp. 136943322098166
Author(s):  
Shuhao Yin ◽  
Bin Rong ◽  
Lei Wang ◽  
Yiliang Sun ◽  
Wuchen Zhang ◽  
...  
Keyword(s):  
Failure Modes ◽  
Plastic Hinge ◽  
Steel Tube ◽  
Nonlinear Finite Element ◽  
Steel Beams ◽  
Finite Element Models ◽  
Test Results ◽  
Panel Zone ◽  
Load Paths ◽  
Shear Performance

This paper studies the shear performance of the connection with the external stiffening ring between the square steel tubular column and unequal-depth steel beams. Two specimens of interior column connections were tested under low cyclic loading. The deformation characteristics and failure modes exhibited by the test phenomena can be summarized as: (1) two specimens all exhibited shear deformation in steel tube web of the panel zone and (2) weld fracture in the panel zone and plastic hinge failure at beam end were observed. Besides, load-displacement behaviors and strain distributions have been also discussed. The nonlinear finite element models were developed to verify the test results. Comparative analyses of the bearing capacity, failure mode, and load-paths between the equal-depth and unequal-depth beam models have been carried out.

scholarly journals Numerical Analysis of the Anisotropy and Scale Effects on the Strength Characteristics of Defected Rockmass

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiabing Liu ◽  
Shaohui He ◽  
Dahai Wang
Keyword(s):  
Compression Test ◽  
Failure Modes ◽  
Scale Effects ◽  
Triaxial Compression ◽  
Influential Factor ◽  
Strength Characteristics ◽  
Uniaxial Compression Test ◽  
Mechanical Parameters ◽  
Strength Parameters ◽  
Strength Behavior

Discontinuous defect in the rockmass is a key influential factor in controlling the strength behavior, and how to estimate the anisotropic strength and scale effect on the defected rockmass is the remaining challenging focus in engineering application. In the present study, intact tuff samples cored from the Xiabeishan tunnel engineering in situ are conducted by experiment tests (i.e., uniaxial compression test, triaxial compression test, and Brazilian tensile test) to obtain the corresponding mechanical parameters. Results from the numerical simulations using the particle flow code (PFC) by the flat-jointed model (FJM) are performed to match the macroparameters from experimental results. It is observed that numerical results have good agreement with the macroscopic mechanical parameters of intact samples including UCS, BTS, triaxial compression strength, and corresponding deformation parameters. Finally, a series of uniaxial and confining compression tests are conducted by using a synthetic rockmass (SRM) method which is coupled with the discrete element method (DEM) and discrete fracture network (DFN). Then, the anisotropy and scale effects on the strength characteristics of the defected rockmass are investigated. The results show that defects have a vital effect on the failure mode and strength behavior of the rockmass in the research region. The strength parameters are changed with the specimen size. The REV size of the considered defected rockmass is regarded as 5 × 10 m, and this size is also influenced by the confinement level. The anisotropy of macroscopic strength parameters is found in the considered defected rockmass, whose stress-strain curves and failure modes are also discussed.

Failure Surfaces for Finitely Strained Two-Phase Periodic Solids Under General In-Plane Loading

2005 ◽  
Vol 73 (3) ◽  
pp. 505-515 ◽  
Author(s):  
N. Triantafyllidis ◽  
M. D. Nestorović ◽  
M. W. Schraad
Keyword(s):  
Variable Stiffness ◽  
Bloch Wave ◽  
Two Phase ◽  
Buckling Mode ◽  
Unit Cells ◽  
First Occurrence ◽  
Order Of Magnitude ◽  
Ultimate Failure ◽  
Periodic Microstructures ◽  
Strain Space

For ductile solids with periodic microstructures (e.g., honeycombs, fiber-reinforced composites, cellular solids) which are loaded primarily in compression, their ultimate failure is related to the onset of a buckling mode. Consequently, for periodic solids of infinite extent, one can define as the onset of failure the first occurrence of a bifurcation in the fundamental solution, for which all cells deform identically. By following all possible loading paths in strain or stress space, one can construct onset-of-failure surfaces for finitely strained, rate-independent solids with arbitrary microstructures. The calculations required are based on a Bloch wave analysis on the deformed unit cell. The presentation of the general theory is followed by the description of a numerical algorithm which reduces the size of stability matrices by an order of magnitude, thus improving the computational efficiency for the case of continuum unit cells. The theory is subsequently applied to porous and particle-reinforced hyperelastic solids with circular inclusions of variable stiffness. The corresponding failure surfaces in strain-space, the wavelength of the instabilities, and their dependence on micro-geometry and macroscopic loading conditions are presented and discussed.

On Failure Mechanisms in Flip Chip Assembly—Part 2: Optimal Underfill and Interconnecting Materials

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Yoonchan Oh ◽  
C. Steve Suh ◽  
Hung-Jue Sue
Keyword(s):  
Time Scale ◽  
Flip Chip ◽  
Thermal Stresses ◽  
Failure Modes ◽  
Scale Effects ◽  
Short Time Scale ◽  
Long Time ◽  
Solder Joint Fatigue ◽  
Scale Properties ◽  
Short Time

The physics explored in this investigation enables short-time scale dynamic phenomenon to be correlated with package failure modes such as solder ball cracking and interlayer debond. It is found that although epoxy-based underfills with nanofillers are shown to be effective in alleviating thermal stresses and improving solder joint fatigue performance in thermal cycling tests of long-time scale, underfill material viscoelasticity is ineffective in attenuating short-time scale propagating shock waves. In addition, the inclusion of Cu interconnecting layers in flip chip area arrays is found to perform significantly better than Al layers in suppressing short-time scale effects. Results reported herein suggest that, if improved flip chip reliability is to be achieved, the compositions of all packaging constituent materials need be formulated to have well-defined short-time scale and long-time scale properties. Chip level circuit design layout also needs be optimized to either discourage or negate short-time wave propagation. The knowledge base established is generally applicable to high performance package configurations of small footprint and high clock speed. The approach along with the numerical procedures developed for the investigation can be a practical tool for realizing better device reliability and thus high manufacturing yield.

scholarly journals Determination of Scale Effects on Mechanical Properties of Berea Sandstone

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hui Li ◽  
Kaoping Song ◽  
Mingguang Tang ◽  
Ming Qin ◽  
Zhenping Liu ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Poisson’S Ratio ◽  
Failure Modes ◽  
Shear Failure ◽  
Scale Effects ◽  
Poisson's Ratio ◽  
Axial Splitting ◽  
Rock Mechanical Properties

The key rock mechanical parameters are strength, elastic modulus, Poisson’s ratio, etc., which are important in reservoir development. The accurate determination of reservoir’s mechanical properties is critical to reduce drilling risk and maximize well productivity. Precisely estimating rock mechanical properties is important in drilling and well completion design, as well as crucial for hydraulic fracturing. Rocks are heterogeneous and anisotropic materials. The mechanical properties vary not only with rock types but also with measurement methods, sample geometric dimensions (sample length to diameter ratio and size), and other factors. To investigate sample scale effects on rock mechanical behaviors, unconfined compression tests were conducted on 41 different geometric dimensions of Berea sandstones; unconfined compressive strength (UCS), Young’s modulus ( E ), Poisson’s ratio ( υ ), bulk modulus ( K ), and shear modulus ( G ) were obtained and compared. The results indicate that sample geometry can significantly affect rock mechanical properties: (1) UCS decreases with the increase of length to diameter ratio (LDR), and the UCS standardize factor is between 0.71 and 1.17, which means -30% to +20% variation of UCS with LDR changing from 1 to 6.7. The test results show UCS exhibits positive relationship with sample size. (2) Young’s modulus slightly increases with LDR increases, while Poisson’s ratio decreases with the increase of LDR. For the tested Berea sandstones, Poisson’s ratio standardizing factor is between 0.57 and 1.11. (3) Bulk modulus of Berea sandstone samples decreases with the increase of LDR, while shear modulus increases with LDR increases. Both bulk modulus and shear modulus increase with the increase of sample size. (4) The principal failure modes were analyzed. The failure modes of the tested Berea sandstones are axial splitting and shear failure. Stocky samples ( LDR < 2 ) tend to go axial splitting, while slender samples ( LDR > 2 ) tend to show shear failure.

A New 3-D Unit Cell Model Used in Homogenization Estimation of Effective Properties of Particle-Filled Composites

2011 ◽  
Vol 374-377 ◽  
pp. 1269-1273
Author(s):  
Yong Ouyang ◽  
Xiao Ling Hu ◽  
Xiu Liu ◽  
Wen Bo Luo
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Cell Model ◽  
Particle Volume Fraction ◽  
Calculated Data ◽  
Effective Elastic Modulus ◽  
Unit Cell ◽  
Unit Cell Model ◽  
Particle Volume ◽  
Periodic Microstructures

A new 3D unit cell model is developed for homogenization calculation of composites containing randomly dispersed ellipsoid inclusions. The new unit cell is constructed using the Ansys Parameter Design Language (APDL), taking the inclusion volume fraction, inclusion orientation and spatial dispersion as variables. A series of unit cells containing multiple ellipsoids, showing random distributions in particle size and position, were constructed and used for finite element calculation at microscale, the effective modulus of the composites with periodic microstructures, which modeled by the unite cells, were then estimated by homogenization. The influences of particle volume fraction and the particle stiffness on the effective elastic modulus of the composites were examined. The estimated results were compared with different particle volume fractions were calculated, and the calculated data was compared with other classic models.

3D-Printable Unit Cell Design for Cubic and Orthotropic Porous Microstructures Using Topology Optimization Based on Optimality Criteria Algorithm

2018 ◽  
Vol 10 (06) ◽  
pp. 1850060 ◽  
Author(s):  
Alireza Moshki ◽  
Akbar Ghazavizadeh ◽  
Ali Asghar Atai ◽  
Mostafa Baghani ◽  
Majid Baniassadi
Keyword(s):  
Topology Optimization ◽  
Optimization Technique ◽  
Optimality Criteria ◽  
Unit Cell ◽  
Topology Design ◽  
Two Phase ◽  
Topology Identification ◽  
Young’S Moduli ◽  
Periodic Microstructures ◽  
Porous Microstructures

Optimal design of porous and periodic microstructures through topology identification of the associated periodic unit cell (PUC) constitutes the topic of this work. Here, the attention is confined to two-phase heterogeneous materials in which the topology identification of manufacturable 3D-PUC is conducted by means of a topology optimization technique. The associated objective function is coupled with 3D numerical homogenization approach that connects the elastic properties of the 3D-PUC to the target product. The topology optimization methodology that is adopted in this study is the combination of solid isotropic material with penalization (SIMP) method and optimality criteria algorithm (OCA), referred to as SIMP-OCA methodology. The fairly simple SIMP-OCA is then generalized to handle the topology design of 3D manufacturable microstructures of cubic and orthotropic symmetry. The performance of the presented methodology is experimentally validated by fabricating real prototypes of extremal elastic constants using additive manufacturing. Experimental evaluation is performed on two designed microstructures: an orthotropic sample with Young’s moduli ratios [Formula: see text], [Formula: see text] and a cubic sample with negative Poisson’s ratio of [Formula: see text]. In all practical examples studied, laboratory measurements are in reasonable agreement with the prescribed values; thus, corroborating the applicability of the proposed methodology.

scholarly journals On the homogenization of a new class of locally periodic microstructures in linear elasticity with residual stress

2017 ◽  
Vol 23 (7) ◽  
pp. 1025-1039
Author(s):  
Brian Seguin
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Broad Class ◽  
Elasticity Tensor ◽  
Unit Cell ◽  
Periodic Homogenization ◽  
New Class ◽  
Effective Elasticity ◽  
Periodic Microstructures ◽  
Macroscopic Equations

Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for which homogenization techniques are available. Motivated by the consideration that such materials are often anisotropic and can possess residual stresses, a broad class of locally periodic microstructures are considered and the resulting effective macroscopic equations are derived. The effective residual stress and effective elasticity tensor are determined by solving unit cell problems at each point in the domain. However, it is found that for a certain class of locally periodic microstructures, solving the unit cell problems at only one point in the domain completely determines the effective elasticity tensor.

scholarly journals Failure Behavior of Hot-Dry-Rock (HDR) in Enhanced Geothermal Systems: Macro to Micro Scale Effects

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hongwei Zhang ◽  
Zhijun Wan ◽  
Derek Elsworth
Keyword(s):  
High Temperatures ◽  
Failure Modes ◽  
Cold Water ◽  
Scale Effects ◽  
Tangent Modulus ◽  
Failure Behavior ◽  
Enhanced Geothermal Systems ◽  
Geothermal Systems ◽  
Rock Structure ◽  
Individual Grains

Evaluations of the mechanical properties and failure modes of granite at high temperatures are important issues for underground projects such as enhanced geothermal systems and nuclear waste disposal. This paper presents the results of laboratory experiments that investigated the physico-mechanical failure behavior of granites at high temperatures. The results allowed several important conclusions to be drawn. Both the uniaxial compressive strength (UCS) and tangent modulus decrease with increasing temperature. Specifically, the UCS-temperature curve can be divided into three sections: a section (20-200°C) where UCS shows a slight decrease, a section (200-300°C) where the UCS decreases significantly, and a third section (300-500°C) where the rate of UCS decrease stabilizes. However, in the entire temperature range from 20 to 500°C, the tangent modulus decreases exponentially. The number of acoustic emission (AE) counts decrease and the counts occur less frequently at higher temperatures. Individual grains are surrounded by a large number of microcracks at 200°C and the crack length increased significantly when heating to 300°C. Specifically, the length of micro-cracks in the granite at 300 °C could be 10 times longer okthan that at 200°C. Quenching or injecting cold water into HDRs would further weaken the rock and induce thermal damage to the rock structure. The strength of rock would be further quench-weakened by 10%, 20% and 30% at 200°C, 300°C and 500°C, respectively. Therefore, in Enhanced/Engineered Geothermal Systems (EGS), quenching is much more destructive than normal thermal stress.

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