Test Specimen Thickness Research Articles

Biaxial bending strength of thin silicon dies in the ring-on-ring test by considering geometric nonlinearity and material anisotropy

The ring-on-ring test (RoR) is a standard biaxial bending test specified in ASTM C1499-19 and ISO 17167. This test has been utilized for characterizing the biaxial bending strength of silicon dies or wafers to eliminate the die edge chipping effect in the four-point bending test. However, judging from the literature, when testing thin silicon dies, the test is subject to geometric nonlinear effects. This study aims to investigate this nonlinear mechanics in the RoR test using experimental, theoretical, and numerical methods while considering silicon material anisotropy. A 2D-isotropy model of a nonlinear finite element method (NFEM) simulation with specimen elastic modulus of 130 GPa is utilized and verified by experiments and a 3D-anisotropy model in terms of deformation (or displacement) and stresses. Based on the 2D-isotropy NFEM solutions, the fitting equations of correction factors to the theoretical solution are proposed and implemented on determining the biaxial bending strength of 10 mm × 10 mm silicon dies ranging from 57 μm to 297 μm in thickness. It is found that those proposed fitting equations are independent on the test specimen thickness, radius, and materials but not on the radii of the loading and supporting rings. It has also been successfully demonstrated that the RoR test using the theory associated with the correction factor equations can be easy to use to determine the biaxial bending strength of the thin silicon dies that frequently failed in the nonlinear range.

Scratch behaviors of polyacrylate-based hard coatings on alternating multi-layered PMMA+PC substrates

In our previous work [1], the scratch behaviors of alternating multi-layered polymethyl methacrylate (PMMA)/polycarbonate (PC) laminates were studied. Generally, a hard coating layer must be introduced to the surface of PMMA + PC laminate to further enhance its hardness and scratch resistance. In this work, the same laminates used in our previous work were coated by a UV-cured polyacrylate hard layer, and the scratch behaviors and relating mechanisms of hard coating (HC) systems were investigated via both progressive normal load scratch test and pencil hardness test. Sliding counterfaces of two tests were stainless steel ball with a diameter of 1 mm and cylinder made of pencil core with a diameter of 2 mm, respectively. Length, width and thickness of test specimen were 150 mm, 33 mm and 1.6 mm, respectively. The effects of HC's thickness and substrate's hardness on scratch behaviors of HC systems were also included. In both scratch tests, experimental results demonstrated that scratch damages of HC systems were featured with dense periodic cracks. Finite element modeling (FEM) revealed that the formation of such crack types was attributed to the maximum principal stress perpendicular to crack propagation direction. Furthermore, it was found that the scratch resistances of HC systems were enhanced as thickness of HC or hardness of substrate increased, the mechanism behind which were found to be decreasing of the maximum principal stress and consequent delaying of crack formation as revealed through FEM.

Hydrogen Permeation in FeCrAl APMT Alloy for Accident Tolerant Fuel Cladding

Iron-chromium-aluminum (FeCrAl) alloys such as APMT (advanced powder metallurgy tubing) are candidate materials to replace zirconium alloys for the light water reactor fuel cladding. This alloy meets the requirements to be a material more tolerant of high-temperature accidents than the current zirconium alloys. One concern is that the use of FeCrAl may result in an increase in tritium presence in the coolant compared to the current design. The aim of the current research was to obtain effective diffusion coefficients (Deff) for hydrogen through APMT using the Devanathan-Stachurski cell. Results showed that at 30°C the Deff value was 2.8 × 10−8 cm2/s. Results also showed a linear relationship between the permeated hydrogen flux and the inverse of the test specimen thickness, which demonstrated the validity of the permeation measurements.

Study on magnetostriction characteristics under different measurement conditions under an externally compressive stress

The measurement of magnetostriction characteristics of grain-oriented electrical steel strip under an external compressive stress has always been a main focus in the process of magnetostriction measurement. There are difficulties in the measurement of magnetostriction, especially under compressive stress, mainly because the thickness of test specimen is small, and the test specimen is very easy to deform under the compressive stress. A weight should be placed on the test specimen to prevent a deformation of the test specimen when the measurement of magnetostriction characteristics under an externally compressive stress according to the IEC/TR 62581:2010. But how much weight and how to place aren’t concerned in IEC standard. In this paper, different weights were placed on the grain-oriented electrical steel test specimen under external compressive stress and zero stress. Through analyzed the measured magnetostriction data under different weights to determine the optimal measurement method of grain-oriented electrical steel strip under compressive stress and zero stress. The purpose of this paper is to find the most accurate and high reproducibility measurement method of magnetostriction, which can truly reflect the magnetostriction performance of grain-oriented electrical steel.

Temperature and test specimen thickness (TST) effect on tensile and fracture behavior of AA2050-T84 alloy

AA2050-T84 is a third-generation Al-Li alloy used for primary structures of the modern transport aircraft wing. Temperature variation is common during flights, and the effect of temperature on the damage tolerance behavior of Al-Li alloys is significant. In the present work, the effect of temperature on tensile and fracture toughness of the AA2050-T84 alloy was tested experimentally. Further, the effect of Test Specimen Thickness (TST) on crack behavior is studied numerically using constraints variation. The Compact Tension (C(T)) specimen was used for linear elastic fracture analysis with variation in thickness to width ratio (B/W) as 0.1, 0.5, and 1. T11 and T33 constraint parameters were used to measure the effect of TST at −20 °C, 24 °C, and 200 °C. Increase in specimen thickness for constant stress intensity factor (KI) resulted in the decrease of T11. However, the T33 increased with an increase in specimen thickness for all temperatures considered. At −20 °C and 24 °C temperatures, the T11 variation was almost identical at all thicknesses. However, a decrease in T11 around 8% was witnessed at 200 °C compared to room temperature. The temperature effect on the T33 variation was steady and marginal. The temperature and TST effect on AA2050-T84 alloy was significant, and the present investigation results are crucial for aircraft design engineers.

Correction factors to strength of thin silicon die in three- and four-point bending tests due to nonlinear effects

The thin silicon dies have been widely used in the three-dimensional integrated circuits (3DIC), stacked-die or wearable electronic packages to meet the requirements of small size, low-profile features, high-pin count, high performance, low-power consumption or even flexibility. The bending strengths of the thin dies cut from silicon wafers have to be determined to ensure no reliability problems, mostly resulting from packaging process handling, reliability testing, and operations. Three-point bending (3PB) and four-point bending (4PB) tests are commonly used for measuring die bending strength; however, both tests are still problematic for testing the thin silicon dies. Therefore, the mechanics of both tests are reevaluated in this study by a nonlinear finite element method (NFEM) with taking into account geometric nonlinearity (or large deflection), associated with the related theoretical formulations. The nonlinear mechanics of both tests are discussed in detail. NFEM results-based correction factors to the linear beam solutions are further proposed in the form of the polynomial fitting equations in this study. Those polynomial fitting equations of the correction factors are proved to be workable and easy to use with an engineering acceptable accuracy. Those correction factors are also found highly dependent on the deflection (δ), span length (L) and radius of roller support (r), but not on test specimen thickness (t) and elastic modulus (E).

Hydrogen embrittlement testing procedure for the analysis of structural steels with Small Punch Tests using notched specimens

The influence of hydrogen on the mechanical properties of three structural steels has been evaluated. A testing procedure based on the Small Punch Test with notched specimens was used to measure hydrogen embrittlement. Two pre-charging methods were applied to introduce hydrogen in the samples. The first method used gaseous hydrogen in a high-pressure reactor at 19.5 MPa and 450 °C for 21 h. The second involved cathodic charging from 2 M H2SO4 + As2O3 electrolyte with a current density of 2 mA/cm2. The results obtained in the Small Punch Tests were compared with those obtained using standard fracture tests. The hydrogen embrittlement behaviour of the different steels, with special attention to the effect of their chemical compositions and microstructures, were compared. The embrittlement indexes obtained with Small Punch Tests are lower than those obtained with standard tests. The low thickness and lower stress triaxiality of the Small Punch Test specimens explains this result. Regardless of the test method used, hydrogen embrittlement grows with the strength of the analysed steel.

A three-dimensional elastic-plastic damage model for predicting the impact behaviour of fibre-reinforced polymer-matrix composites

A three-dimensional (3-D) Finite Element Analysis (FEA) model incorporating an elastic-plastic (EP) damage model, which was implemented as a user-defined material (‘VUMAT’) sub-routine in a FEA code (‘Abaqus/Explicit’), is developed to simulate the impact response of carbon-fibre reinforced-plastic (CFRP) composites. The model predicts the load versus time and the load versus displacement responses of the composite during the impact event. Further, it predicts the extent, shape and direction of any intralaminar damage and interlaminar delaminations, i.e. interlaminar cracking, as a function of the depth through the thickness of the impacted CFRP test specimen, as well as the extent of permanent indention caused by the impactor striking the composite plate. To validate the model, experimental results are obtained from relatively low-velocity impact tests on CFRP plates employing either a matrix of a thermoplastic polymer, i.e. poly(ether-ether ketone), or a thermosetting epoxy polymer. The 3-D EP model that has been developed is shown to model successfully the experimentally-measured impact behaviour of the CFRP composites.

Geometric Nonlinear Effect on Biaxial Bending Strength of Thin Silicon Die in the PoEF Test

The easy-to-use point-load on elastic foundation (PoEF) test, similar (or alternative) to a typical biaxial bending ball-on-ring test, is studied for determining the bending strength of thin silicon dies. The feasibility of this test method with a linear theory is also evaluated using a nonlinear finite element method (NFEM) by taking into account geometric and contact nonlinearities. The mechanics of the PoEF test is discussed in terms of geometric linearity and nonlinearity. The results show that the geometric nonlinearity would cause significant errors of bending strength data, due to the maximum applied stress moving away from the loading pin center, if the linear theory is applied for thin die specimens in this test. The comprehensive fitting equations based on the NFEM results, with better accuracy than the linear theory, are proposed for calculating the thin die strength. Some key parameters, including the head radius of the loading pin ( ${r}$ ), elastic modulus of the foundation ( $E_{EF}$ ), elastic modulus of the test specimen ( ${E}$ ), and test specimen thickness ( ${t}$ ), are also discussed individually by studying their effects on the fitting equations. In an experimental implementation, the thin silicon die specimens with various thicknesses are actually performed in the PoEF test. It is found that the thinner specimen suffers from more severe geometric nonlinearity effect. The statistical strength data converted by the fitting equations are demonstrated and show that the geometric nonlinearity has to be taken into account in the PoEF test when the thin specimens are tested. The ready-to-use fitting equations proposed in this study are proved to be viable solutions for the conversion of those nonlinear test data.

Evaluation of Three-Point Bending Strength of Thin Silicon Die With a Consideration of Geometric Nonlinearity

With the trends of electronic packaging development toward small size, low-profile features, high-pin count, and high performance, the 3D IC (Three-dimensional Integrated Circuits) or stacked-die packages have been gaining popularity. For such package applications, IC silicon wafers have to be ground and processed to be relatively thin and then the thin silicon dies cut from these wafers have to gain sufficient strength in order to bear high stresses resulting from process handling, reliability testing, and operations. Hence, the strength of the thin dies has to be determined to ensure the good reliability of the packages. Three-point bending test is commonly used for measuring die strength; however, the feasibility of the test is still questionable for determining the strength of relatively thin dies. Therefore, the feasibility of the linear beam theory is evaluated by a nonlinear finite element method (NFEM) with taking into account geometric nonlinearity in this study. The results show that this nonlinearity would cause errors of the strength of thin dies if calculated by the linear beam theory. The fitting equations of the correction factors ( $\eta $ ) to linear solutions, extracted from the NFEM simulation, are proposed and proved to be workable with very good accuracy. It is also found that the correction factor highly depends on the deflection ( $\delta $ ), span length (L) and radius of roller support (r), but not elastic modulus (E) and thickness (t) of test specimens. After the nonlinearity has to be taken into account for the relatively thin silicon dies, the consistent statistical strength data have been obtained for various thicknesses of the test die specimens.

Characterization of pulsed eddy current signals to discriminate cladding change over wall thinning of ferromagnetic pipes

Pulsed eddy current (PEC) testing technique is regarded as the most effective nondestructive evaluation method used to measure wall thinning through multiple layer and irregular surface objects. When the test specimen is covered with insulation and shielded with thin aluminum, PEC technique became advantageous to completely illustrate structural variations. However, the interpretation of PEC signal seems complex when the specimen is insulated and externally cladded with aluminum sheet, since variations in aluminum thickness and wall thinning results into similar effect on PEC signal. In this study, the focal point is to detect the pipe wall-thinning through insulation and aluminum cladding, another important objective is to characterize the cladding and test specimen thickness change.

Evaluation of the Low Temperature Properties of Asphalt Mixtures Using a Digital Image Correlation Approach

Abstract Asphalt concrete performance hinges on its cracking resistance. Numerous test methods have been used to consider fracture of asphalt concrete at intermediate and low temperatures. All focus on global mixture measurements of load and displacement at a discrete location on the test specimen. Digital image correlation (DIC) measurements provide a means to evaluate the full-field response of asphalt concrete undergoing fracture. In particular, several studies have employed DIC to quantify the size of strain localization as a potential definition of the fracture process zone (FPZ). The current study evaluated the low temperature fracture properties of asphalt concrete using the disk-shaped compact tension (DC(T)) test (ASTM D7313-13) and in-plane DIC-measured FPZ size. Tests were completed to compare the sizes of the FPZ with respect to the test specimen thickness, aging of neat and polymer-modified asphalt mixtures, maximum aggregate size, and reclaimed asphalt pavement (RAP) content. Results in the current study found that DIC measurements differentiated the size of the FPZ in terms of polymer modification, aging, and RAP content.

応力分布Tスケーリング法適用による圧縮残留応力付与時破壊靭性値の予測

The fracture toughness Jc of the material in the ductile to brittle transition temperature (DBTT) region shows test specimen thickness (TST) effect and temperature dependence, and apparently increases when compressive residual stress is applied. In this paper, as TST effect and temperature dependence, the fact that Jc apparently increases due to compressive residual stress is attributable to the loss in the one-to-one correspondence between J and the crack-tip stress distribution, and then, the fracture prediction of the specimen with compressive residual stress was performed using the T-scaling method proposed by the authors, and its validity was confirmed for high strength steel of 780 MPa class and 0.45 % carbon steel JIS S45C. In addition, it was suggested that the minimum of Jc with compressive residual stress can be predicted by requiring only the tensile test.

3D Stress intensity factor and T-stresses (T11 and T33) formulations for a Compact Tension specimen

The paper describes test specimen thickness effect on stress intensity factor (KI), and T-stresses stresses (T11 and T33) for a Compact Tension specimen. Formulations to estimate 3D KI, T11 and T33 stresses are proposed based on extensive 3D Finite element analyses. These formulations help to estimate magnitudes of 3D KI and T11 and T33 which are helpful to quantify in-plane and out-of- plane constraint effect of the crack tip. The proposed formulations are validated with the similar results available in literature and found to be within acceptable error.

Applicability of the modified Ritchie–Knott–Rice failure criterion to transfer fracture toughness Jc of reactor pressure vessel steel using specimens of different thicknesses—Possibility of deterministic approach to transfer the minimum Jc for specified specimen thicknesses

The validity of the modified Ritchie–Knott–Rice failure criterion to transfer the fracture toughness Jc of a reactor pressure vessel steel material was examined using specimens with thicknesses in the range of 8–254mm. Here, the modified Ritchie–Knott–Rice criterion is the (4δt, σ22c) criterion, which predicts the onset of cleavage fracture when the crack-opening stress σ22 measured at a distance from the crack tip equal to four times the crack-tip opening displacement δt, denoted as σ22d, exceeds a critical value σ22c. Large-strain elastic–plastic finite element analysis was performed to reproduce the fracture toughness (Jc) test results of 21 SE(B) specimen types and 141 specimens satisfying the ASTM E1921 requirements of M=(b0σYS)/Jc⩾30 and 0.45⩽a/W⩽0.55, where b0 is the initial ligament size, σYS is the yield stress, and a/W is the crack depth-to-width ratio. The material was reactor pressure vessel ASTM A533 Grade B class 1 steel, and tests were conducted in the ductile-to-brittle transition temperature region. The results show that the modified Ritchie–Knott–Rice failure criterion is valid for specimens of various thicknesses, although in this study, the constraint differences were small. The critical value σ22c showed only 4.6% variation, and its probabilistic nature appeared to be negligible. The effect of the test specimen thickness on Jc was concluded to result from the inability of J to characterize the crack-tip stress fields accurately. Although further investigation of the application limit of the (4δt, σ22c) criterion is necessary, the results appear to show that the critical value σ22c is a deterministic value corresponding to the minimum Jc observed for a specific specimen, which can be determined by the specimen geometry and tensile property of the material. Because application of the (4δt, σ22c) failure criterion requires only a single specimen or set of test data, whereas calibration of the Weibull stress in the probabilistic approach requires many specimens, the deterministic approach using the (4δt, σ22c) criterion may be suitable for use in place of the probabilistic approach using the Weibull stress in certain circumstances, such as in the cases that the minimum Jc is of main interest.

工業用純鉄の伸びおよび変形エネルギーに及ぼす引張試験片板厚の影響

工業用純鉄の伸びおよび変形エネルギーに及ぼす引張試験片板厚の影響

Evaluation and effect of loss of constraint on master curve reference temperature of 20MnMoNi55 steel

The effect of test temperature, specimen thickness and crack to width ratio on master curve reference temperature in ductile to brittle transition range of 20MnMoNi55 steel is experimentally determined. To transfer the correlations from specimen to component level, the effect of loss of constraint on reference temperature is estimated through triaxiality ratio using finite element analysis. The experimental fracture toughness tests are simulated in ABAQUS and the value of triaxiality ratio is computed at failure loads and the same is used to characterize the effect of constraint on master curve reference temperature.

二相ステンレス鋼の変形エネルギーに及ぼす引張試験片板厚の影響

二相ステンレス鋼の変形エネルギーに及ぼす引張試験片板厚の影響

Extended investigation of the test specimen thickness (TST) effect on the fracture toughness (Jc) of a material in the ductile-to-brittle transition temperature region as a difference in the crack tip constraint − What is the loss of constraint in the TST effects on Jc?

This paper answers a question that was raised from our recent work [1] for the non-standard single-edge notched bend (SE(B)) specimens, which exhibited the test specimen thickness effect on Jc (TST effect on Jc) together with the bounded nature for increasing TST in the ductile-to-brittle transition temperature region. The question was “what is the loss of constraint in the TST effect on Jc, because the crack opening stress σ22 distribution scaled with CTOD at fracture load was approximately same for different TSTs?”To answer this question, several well-known constraint parameters were investigated to determine their correlations with the TST effect and the bounded nature of Jc for increasing TST. Based on the elastic–plastic finite element analysis results, it was demonstrated that the well-known stress triaxiality factor Θ=(hydrostatic stress)/(von Mises stress), measured at 4δtc (crack-tip opening displacement at fracture load Pc), exhibited a good correlation with the decreasing and subsequently bounded nature of Jc for increasing TST. Θ started to decrease at some load level before fracture for relatively thin specimens, and this was the loss of constraint in the TST effects on Jc.

Application ofT33-Stress to Predict the Lower Bound Fracture Toughness for Increasing the Test Specimen Thickness in the Transition Temperature Region

This work was motivated by the fact that although fracture toughness of a material in the ductile-to-brittle transition temperature regionJcexhibits the test specimen thickness (TST) effect onJc, frequently described asJc∝(TST)-1/2, experiences a contradiction that is deduced from this empirical formulation; that is,Jc= 0 for large TST. On the other hand, our previous works have showed that the TST effect onJccould be explained as a difference in the out-of-plane constraint and correlated with the out-of-planeT33-stress. Thus, in this work, the TST effect onJcfor the decommissioned Shoreham reactor vessel steel A533B was demonstrated from the standpoint of out-of-plane constraint. The results validated thatT33was effective for describing theJcdecreasing tendency. Because the Shoreham data included a lower boundJcfor increasing TST, a new finding was made thatT33successfully predicted the lower bound ofJcwith increasing TST. This lower boundJcprediction withT33conquered the contradiction that the empiricalJc∝(TST)-1/2predictsJc= 0 for large TST.