A Thermo-Viscoelastic Analysis and Reliability Evaluation for a Single-Sided CSP

2005 ◽  
Author(s):  
Hideo Koguchi ◽  
Mirai Ishida ◽  
Kazuto Nishida ◽  
Tomoaki Kuroishi
Keyword(s):  
Normal Stress ◽  
Viscoelastic Properties ◽  
Normal Stresses ◽  
Layered Plate ◽  
Heat Cycle ◽  
Viscoelastic Analysis ◽  
Chip Size ◽  
Properties Of Materials ◽  
Rigid Walls ◽  
Gold Bump

In the present paper, a reliability of a single-sided chip-size package (CSP) manufactured using a non-conductive adhesive stud bump direct interconnection method is investigated. The reliability of the CSP is closely related with normal stress between an IC chip and a gold bump. Total normal stress can be decomposed into two parts, deflection related and thermal expansion related. The deflection for a three-layered plate, which is taken into account viscoelastic properties for the resin-sealed sheet and the substrate, respectively, is calculated and compared with experimental results on the deflection of the single-sided CSP. A relationship between the normal stress and the curvature derived from deflection is deduced. Through the use of this relationship, the variation of normal stress with the heat cycle is obtained considering the viscoelastic properties of materials. Furthermore, a relaxation behavior for the thermal stress in the resin-sealed sheet between two rigid walls considering its viscoelastic property is investigated. Summing up normal stresses for each calculation yields the normal stress between the IC and the bump. A relationship between the normal stress and the life of single-sided CSP is investigated for heat cycle. The life in experiment can be explained by the relaxation in the normal stress and the amplitude of the normal stress.

Thermo-Viscoelastic Analysis for Warpage in CSP With Different Viscoelastic Properties for Several Layers

2007 ◽  
Author(s):  
Hideo Koguchi ◽  
Atsushi Ueno
Keyword(s):  
Thermal Expansion ◽  
Theoretical Analysis ◽  
Manufacturing Process ◽  
Viscoelastic Properties ◽  
Layered Material ◽  
Viscoelastic Analysis ◽  
Chip Size ◽  
The Difference ◽  
On Chip ◽  
Layered Body

In this study, a simple theory for estimating the warpage of chip size packaging (CSP) during a manufacturing process is presented. A single-sided CSP which is composed of IC, a resin and a substrate is modeled for an analysis as a three-layered material. Especially, the resin and the substrate have different thermo-viscoelastic properties. When the layered body is perfectly bonded, its warpage is caused by the difference of the thermal expansion coefficient in each layer when temperature varies. The warpage of CSP for a various thicknesses of the IC and the substrate is investigated. Finally, the warpage calculated using the theory is compared with the result in experiment, and both results are well agreed with each other. Then, it is shown that the simple theoretical analysis is valid. After that, this program is extended to be able to analyze the warpage in a CoC (Chip on Chip), and the result of the analysis is then presented.

scholarly journals Rock Stress Measurements for Unlined Pressure Tunnels: A True Triaxial Laboratory Experiment to Investigate the Ability of a Simplified Hydraulic Jacking Test to Assess Fracture Normal Stress

2021 ◽  
Author(s):  
Henki Ødegaard ◽  
Bjørn Nilsen
Keyword(s):  
Normal Stress ◽  
Test Method ◽  
Sudden Increase ◽  
Normal Stresses ◽  
True Triaxial ◽  
Step Rate ◽  
Stress Measurements ◽  
Fracture Closure ◽  
Rate Test ◽  
Hydraulic Jacking

AbstractTo avoid hydraulic failure of unlined pressure tunnels, knowledge of minimum principal stress is needed. Such knowledge is only obtainable from in situ measurements, which are often time-consuming and relatively costly, effectively limiting the number of measurements typically performed. In an effort to enable more stress measurements, the authors propose a simplified and cost-effective stress measuring method; the Rapid Step-Rate Test (RSRT), which is based on existing hydraulic testing methods. To investigate the ability of this test to measure fracture normal stresses in field-like conditions, a true triaxial laboratory test rig has been developed. Hydraulic jacking experiments performed on four granite specimens, each containing a fracture, have been performed. Interpretation of pressure-, flow- and acoustic emission (AE) data has been used to interpret fracture behaviour and to assess fracture normal stresses. Our experimental data suggest that the proposed test method, to a satisfactory degree of reliability, can measure the magnitude of fracture normal stress. In addition, a clear correlation has been found between fracture closure and sudden increase in AE rate, suggesting that AE monitoring during testing can serve as a useful addition to the test. The rapid step-rate test is also considered relevant for field-scale measurements, with only minor adaptions. Our findings suggest that the RSRT can represent a way to get closer to the ideal of performing more testing along the entire length of pressure tunnel, and not only at key locations, which requires interpolation of stress data with varying degree of validity.

Shear strength and dilative characteristics of an unsaturated compacted completely decomposed granite soil

2010 ◽  
Vol 47 (10) ◽  
pp. 1112-1126 ◽  
Author(s):  
Md. Akhtar Hossain ◽  
Jian-Hua Yin
Keyword(s):  
Shear Strength ◽  
Normal Stress ◽  
Matric Suction ◽  
Water Retention Curve ◽  
Direct Shear ◽  
Normal Stresses ◽  
Soil Water Retention Curve ◽  
Strength Data ◽  
Decomposed Granite ◽  
Completely Decomposed Granite

Shear strength and dilative characteristics of a re-compacted completely decomposed granite (CDG) soil are studied by performing a series of single-stage consolidated drained direct shear tests under different matric suctions and net normal stresses. The axis-translation technique is applied to control the pore-water and pore-air pressures. A soil-water retention curve (SWRC) is obtained for the CDG soil from the equilibrium water content corresponding to each applied matric suction value for zero net normal stress using a modified direct shear apparatus. Shear strength increases with matric suction and net normal stress, and the failure envelope is observed to be linear. The apparent angle of internal friction and cohesion intercept increase with matric suction. A greater dilation angle is found at higher suctions with lower net normal stresses, while lower or zero dilation angles are observed under higher net normal stresses with lower suctions, also at a saturated condition. Experimental shear strength data are compared with the analytical shear strength results obtained from a previously modified model considering the SWRC, effective shear strength parameters, and analytical dilation angles. The experimental shear strength data are slightly higher than the analytical results under higher net normal stresses in a higher suction range.

scholarly journals A temperature- and stress-controlled failure criterion for ice-filled permafrost rock joints

2018 ◽  
Vol 12 (10) ◽  
pp. 3333-3353 ◽  
Author(s):  
Philipp Mamot ◽  
Samuel Weber ◽  
Tanja Schröder ◽  
Michael Krautblatter
Keyword(s):  
Normal Stress ◽  
Failure Criterion ◽  
Slope Failure ◽  
Rock Slope ◽  
Shear Resistance ◽  
Stress Conditions ◽  
Rock Joints ◽  
Normal Stresses ◽  
Permafrost Rock ◽  
Limestone Sample

Abstract. Instability and failure of high mountain rock slopes have significantly increased since the 1990s coincident with climatic warming and are expected to rise further. Most of the observed failures in permafrost-affected rock walls are likely triggered by the mechanical destabilisation of warming bedrock permafrost including ice-filled joints. The failure of ice-filled rock joints has only been observed in a small number of experiments, often using concrete as a rock analogue. Here, we present a systematic study of the brittle shear failure of ice and rock–ice interfaces, simulating the accelerating phase of rock slope failure. For this, we performed 141 shearing experiments with rock–ice–rock “sandwich”' samples at constant strain rates (10−3 s−1) provoking ice fracturing, under normal stress conditions ranging from 100 to 800 kPa, representing 4–30 m of rock overburden, and at temperatures from −10 to −0.5 ∘C, typical for recent observed rock slope failures in alpine permafrost. To create close to natural but reproducible conditions, limestone sample surfaces were ground to international rock mechanical standard roughness. Acoustic emission (AE) was successfully applied to describe the fracturing behaviour, anticipating rock–ice failure as all failures are predated by an AE hit increase with peaks immediately prior to failure. We demonstrate that both the warming and unloading (i.e. reduced overburden) of ice-filled rock joints lead to a significant drop in shear resistance. With a temperature increase from −10 to −0.5 ∘C, the shear stress at failure reduces by 64 %–78 % for normal stresses of 100–400 kPa. At a given temperature, the shear resistance of rock–ice interfaces decreases with decreasing normal stress. This can lead to a self-enforced rock slope failure propagation: as soon as a first slab has detached, further slabs become unstable through progressive thermal propagation and possibly even faster by unloading. Here, we introduce a new Mohr–Coulomb failure criterion for ice-filled rock joints that is valid for joint surfaces, which we assume similar for all rock types, and which applies to temperatures from −8 to −0.5 ∘C and normal stresses from 100 to 400 kPa. It contains temperature-dependent friction and cohesion, which decrease by 12 % ∘C−1 and 10 % ∘C−1 respectively due to warming and it applies to temperature and stress conditions of more than 90 % of the recently documented accelerating failure phases in permafrost rock walls.

On the Applicability of Sneddon's Solution for Interpreting the Indentation of Nonlinear Elastic Biopolymers

2014 ◽  
Vol 81 (9) ◽  
Author(s):  
Man-Gong Zhang ◽  
Jinju Chen ◽  
Xi-Qiao Feng ◽  
Yanping Cao
Keyword(s):  
Elastic Properties ◽  
Viscoelastic Properties ◽  
Contact Theory ◽  
Elastic Contact ◽  
Flat Punch ◽  
Linear Elastic ◽  
Contact Models ◽  
Properties Of Materials ◽  
Nonlinear Elastic ◽  
Viscoelastic Contact

Indentation has been widely used to characterize the mechanical properties of biopolymers. Besides Hertzian solution, Sneddon's solution is frequently adopted to interpret the indentation data to deduce the elastic properties of biopolymers, e.g., elastic modulus. Sneddon's solution also forms the basis to develop viscoelastic contact models for determining the viscoelastic properties of materials from either conical or flat punch indentation responses. It is worth mentioning that the Sneddon's solution was originally proposed on the basis of linear elastic contact theory. However, in both conical and flat punch indentation of compliant materials, the indented solid may undergo finite deformation. In this case, the extent to which the Sneddon's solution is applicable so far has not been systematically investigated. In this paper, we use the combined theoretical, computational, and experimental efforts to investigate the indentation of hyperelastic compliant materials with a flat punch or a conical tip. The applicability of Sneddon's solutions is examined. Furthermore, we present new models to determine the elastic properties of nonlinear elastic biopolymers.

Normal stresses and microstructure in bounded sheared suspensions via Stokesian Dynamics simulations

2000 ◽  
Vol 412 ◽  
pp. 279-301 ◽  
Author(s):  
ANUGRAH SINGH ◽  
PRABHU R. NOTT
Keyword(s):  
Normal Stress ◽  
Couette Flow ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Normal Stresses ◽  
Plane Couette Flow ◽  
Stokesian Dynamics ◽  
First Normal Stress Difference ◽  
Particle Pressure ◽  
Dynamics Simulations

We report the normal stresses in a non-Brownian suspension in plane Couette flow determined from Stokesian Dynamics simulations. The presence of normal stresses that are linear in the shear rate in a viscometric flow indicates a non-Newtonian character of the suspension, which is otherwise Newtonian. While in itself of interest, this phenomenon is also important because it is believed that normal stresses determine the migration of particles in flows with inhomogeneous shear fields. We simulate plane Couette flow by placing a layer of clear fluid adjacent to one wall in the master cell, which is then replicated periodically. From a combination of the traceless hydrodynamic stresslet on the suspended particles, the stresslet due to (non-hydrodynamic) inter-particle forces, and the total normal force on the walls, we determine the hydrodynamic and inter-particle force contributions to the isotropic ‘particle pressure’ and the first normal stress difference. We determine the stresses for a range of the particle concentration and the Couette gap. The particle pressure and the first normal stress difference exhibit a monotonic increase with the mean particle volume fraction ϕ. The ratio of normal to shear stresses on the walls also increases with ϕ, substantiating the result of Nott & Brady (1994) that this condition is required for stability to concentration fluctuations. We also study the microstructure by extracting the pair distribution function from our simulations; our results are in agreement with previous studies showing anisotropy in the pair distribution, which is the cause of normal stresses.

scholarly journals Numerical Analysis for the Progressive Failure of Binary-Medium Interface under Shearing

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Rihong Cao ◽  
Wenyu Tang ◽  
Hang Lin ◽  
Xiang Fan
Keyword(s):  
Shear Strength ◽  
Bond Strength ◽  
Normal Stress ◽  
Strength Ratio ◽  
Normal Stresses ◽  
Stress Increase ◽  
Tensile Cracks ◽  
Medium Interface ◽  
High Bond ◽  
High Bond Strength

Binary-medium specimens were fabricated using the particle flow code, and the shear strength, dilatancy, and failure behavior of the binary-medium specimens with different bond strength ratios (0.25, 0.5, 0.75, and 1.0) under different normal stresses were studied. Numerical results show that the bond strength ratio and normal stresses considerably influence the shear strengths of binary-medium interface. Shear strength increases as the bond strength ratio and normal stress increase. The dilation of interfaces with high bond strength ratios is more evident than those of interfaces with lower bond strength ratios, and the curves for the high bond strength ratio exhibit remarkable fluctuations during the residual stage. At increased normal stress and bond strength ratio, the peak dilation angle shows decreasing and increasing trends successively. In this study, the specimens exhibited three kinds of failure modes. In mode II, the sawtooth experienced shear failure, but some tensile cracks appeared on the interface of the binary-medium. In mode III, no sawtooth was cut off, indicating tensile failure on the interface. At a low bond strength ratio, damage or failure is mostly concentrated in the upper part of the model. Failure parts gradually transfer to the lower part of the model when the bond strength ratio and normal stress increase. Furthermore, evident tensile cracks occur on the interface. When the bond strength ratio reaches 1.0, the failure mode of the specimen gradually transforms from sheared-off failure to chip-off failure. The number of microcracks in the specimens indicates that the lower the bond strength ratio, the more severe the damage on the specimens.

scholarly journals Shear Mechanical Behaviours and Multistrength Parameter Characteristics of Fault Gouge

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Han Bao ◽  
Qun Qi ◽  
Hengxing Lan ◽  
Changgen Yan ◽  
Wei Xu ◽  
...  
Keyword(s):  
Water Content ◽  
Normal Stress ◽  
Clay Minerals ◽  
Residual Strength ◽  
Failure Modes ◽  
Friction Angle ◽  
Strength Properties ◽  
Fault Gouge ◽  
Normal Stresses ◽  
Fault Gouges

Fault gouge has special mechanical properties and remarkable engineering effects. Using a ring shear test, the strength properties of the differently colored remolded fault gouges of the Shendaogou Fault in Yan’an were studied by changing moisture contents and normal stresses. Chlorite and illite are the main clay minerals in fault gouges; differences in mineral composition make fault gouges appear in different colors. Besides clay minerals, the dried fault gouges disintegration in water is also due to the transformation of gypsum. The gradation of green fault gouge and multicolor fault gouge is better than that of the red fault gouge, while the fault gouges’ strain softening properties become weaker as the coarse grain content increases. Affected by water content and normal stress, the shear planes can be divided into three failure modes: peeling failure, grooved failure, and sliding failure. With the increase of water content, there will be a significant weakening on cohesion and friction angle. A new parameter, the “Normal Stress Threshold (NST),” is introduced as a critical value for the emergence of the strain hardening phenomenon, and the NSTs of different fault gouges are significantly different. The functions obtained from the relation of residual strength, peak strength, and normal stress can be used to calculate shear strength parameters under any normal stresses. In addition, the residual strength of fault gouge is obviously different from clay and loess, which can be qualitatively explained by clay particle contents.

Sign in / Sign up

Export Citation Format

Share Document