Moire Data Research Articles

Warpage Modeling of Ultra-Thin Packages Based on Chemical Shrinkage and Cure-Dependent Viscoelasticity of Molded Underfill

Molded underfill (MUF) is an essential component in ultra-thin flip chip packages to ensure their long-term reliability and mechanical integrity. However, the warpage evolution of package during the curing process of MUF has a critical effect on both the SMT yield and package reliability. Therefore, a thorough understanding of the MUF physical behavior under curing is essential. The present study therefore successfully establishes a novel process modeling approach based on finite element method to predict the final warpage of an ultra-thin flip chip scale package (fcCSP) in accordance with the chemical shrinkage and cure-dependent viscoelastic behavior of MUF. In describing the cure-dependent behavior of the MUF, the chemical shrinkage, curing kinetics and time-domain viscoelasticity are characterized by the pressure-volume-temperature (PVT) method, differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA), respectively. The predicted package warpage results are shown to be in good agreement with the experimental thermal Shadow Moire data. It is additionally shown that the accuracy of the warpage predictions is seriously degraded if the mechanical properties of MUF is modeled using a simple temperature-dependent elastic assumption.

Analysis of moiré data for near-interface cracks

The analysis of moire data obtained in bimaterials with near-interface cracks is examined. To extract stress intensity factors, a collocation-type method is developed where Westergaard crack-tip expansions are used for displacements in the cracked portion of the bimaterial, expansions from the method of fundamental solutions are used for displacements in the uncracked portion of the bimaterial, and continuity conditions at the interface are used to couple the two expansions. Proof-of-principle numerical experiments performed on synthetic data from a boundary element analysis of a cracked bimaterial successfully demonstrated the analysis method. Mixed-mode stress intensity factors were then determined from actual moire data obtained in a copper–tungsten specimen.

GS(2)-6(GSW0153) CTOA of a Tunneling Crack-a Hybrid Analysis

A hybrid moire-finite element analysis (FEA) method was used to determine the crack tip opening angle (CTOA) along a tunneling crack front in a three-point bend (SEB) specimen. The specimen was machined from a ductile 2024-T351 aluminum plate of 8.1 mm thickness and was pre-fatigued to an initial crack length, α_0,of α_0/W=0.45. The specimen was subjected to stable crack growth varying Δα=0.5 to 5.5 mm, after which the specimen was post fatigued to mark the final crack front and then loaded to failure. The changes in the μ-and ν-displacement fields on the specimen surface with increasing load and crack growth were recorded by moire interferometry. The crack profiles from five broken specimens were assembled to compose sequential tunneling crack profiles in a single specimen. A quarter segment of the SEB specimen was modeled with a truncated 3-D elastic-plastic FEA model for computational efficiency. A preliminary 3-D elastic-plastic analysis of the full half segment with α/W=0.45 was used to determine the minimum distance from the crack plane at which the von-Mises stress is uniform through the specimen thickness. The span-wise length of the truncated FEA model, with a minimum element of 0.25 mm cube, was set to this distance. The measured surface displacements, which were obtained by moire analysis, with successively increasing load and incremental stable crack growth were prescribed on the truncated edge. The CTOA was obtained from the computed crack opening displacement, approximately 1 mm behind, and normal to the crack front. The figures below show the CTOA variations with local crack extension on the surface, length-wise quarter-and mid-planes of the SEB specimen. CTOA obtained directly from the moire data is included for comparison. The good agreement between the measured and computed surface CTOA are indicative of the accuracy of the procedure.

A multilevel treatment of moiré fringe data using finite elements

Finite element procedures are applied to the modeling, analysis and visualization of experimental moire data. Smoothing elements are introduced and evaluated with respect to data sparseness and error. A one-dimensional smoothing element is uniquely coupled with the method of principal curves to extract moire fringe centers. A two-dimensional smoothing element is then used to produce a full-field representation given the fringe locations. The moire technique is applied to the four-point bend experiment, and the surface-modeling technique is used to obtain displacement and gradient (strain) information.

In-plane shear testing of graphite-woven fabric composites

The losipescu shear test method was used to determine the in-plane shear response of AS4 and Celion carbon fiber/epoxy fabric composite materials. Several weave architectures were studied: AS4 uniweave, AS4 and Celion plain weaves, Celion 5-harness and 8-harness satin weaves. Specimens were tested using traditional strain gage techniques and full-field moire interferometry. A full-node localized hybrid analysis is introduced to perform efficient reduction of moire data, producing whole-field strain distributions in the specimen test section. It was found that the fabric yarn size greatly influenced the uniformity of the shear field in the specimen test section. However, consistent shear moduli still can be obtained using the modified losipescu specimen and Wyoming fixture except for fabrics with large fiber yarns.

A technique for experimental evaluation of mixed mode stress intensity factors

High sensitivity moire interferometry was used to obtain whole-field orthogonal components of displacement in the vicinity of cracks in centre-cracked plates of aluminium 6082. The plates had been prepared in such a way as to enable the application of load at angles of 75° and 60° to the planes of the fatigue pre-cracks. The form of the moire fringe data enables convenient separation of the components of stress intensity factor K I and K II. The results are compared with analytical predictions. The method is, in principle, suitable for use with specimens of arbitrary geometry and loading.

Experimental investigation of creep-crack-tip deformation using moiré interferometry

High-temperature moire interferometry was applied to obtain full-field creep-crack-tip displacements of a three-point bend Al 2024-T4 specimen uner constant temperature of 200°C up to 720 hr.C * was evaluated by the moire data obtained at discrete time intervals. Test results indicate that under steady-state creep condition, the creepcrack-tipv-displacement rate agrees with the asymptotic solution based on theC * integral. However, no creeping behavior was observed for the crack-tipu-displacement field aftert=276 hr. This discrepancy may be due to the initial large creep-crack-tip blunting and cavitation damage which alter the creep-crack-tip singular field such that theC * integral is no longer applicable to characterize the steady-state creep-crack-tip field. Postmortem studies of the tested specimen also revealed transgranular fracture path with the ordered grain boundaries perpendicular to the crack line, which may relate to the existence of the substantial crack-tip blunting and noncreeping behavior of theu-displacement field, i.e., the size and shape of material grain boundaries play an important role in the crack-tip-creeping behavior of the material.

An experimental investigation of losipescu specimen for composite materials

A detailed experimental evaluation of the losipescu specimen tested in the modified Wyoming fixture is presented. Moire interferometry is employed to determine the deformation of unidirectional and cross-ply graphite-epoxy specimens. The results of the moire experiments are compared to those from the traditional strain-gage method. It is shown that the strain-gage readings from one surface of a specimen together with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to twisting. A localized hybrid analysis is introduced to perform efficient reduction of moire data, producing whole-field strain distributions in the specimen test sections.

Temperature and/or density measurements of asymmetrical flow fields by means of the moire-schlieren method. (1st report. Inverting method of moire data using an orthogonal polynominal expansion.

A numerical method is presented for inverting the moire data which represent integral light deflection to internal temperature and /or density distributions. The method is applicable to both symmetrical and asymmetrical flow field. The inverting method is constructed on the basis of the Maldonado-Olsen series representation which was developed for the inversion of an integral intensity fields. The validity and accuracy of the present method have been demonstrated by using a mathematical model with a density function of a truncated pyramid type.

Characterization of Strain Fields Around Weld Defects

Moire interferometry is used as an alternate technique to resistance strain gages in finding full-field, local strain response of weldments to applied loads. The principles of moire interferometry and the experimental set-up are explained. Data from the two techniques are compared, with no major discrepancies. The strain field around a surface defect is analyzed using moire data. It is concluded that the moire technique is useful for obtaining full-field strain data in welds.

Application of moire technique in fracture analysis

Abstract In the present paper, an improvement on the traditional treatment method for moire data is made, and the so-called surface-fitting process is used to treat the moire data. A method of measurement of J- integrals from moire data is proposed, which can be used for pressure vessels and other shell structures. By means of the proposed method, J- integrals of different contours are calculated with centrally cracked wide plates under different loading conditions. The J- integrals calculated by the proposed method are in good agreement with those calculated by the Rice formula, both being based upon the present authors' same experiments.

Temperature mapping in flames by moire deflectometry

The theory of moire deflectometry is derived using the Fourier series approach. The advantages and disadvantages of the infinite fringe limit are demonstrated. The approach of fringe deviation is compared to the intensity measurement, which is selected as being more suitable for flames. An experimental technique based on pointwise scanning is developed to obviate the deficiencies of the video system used previously. Moire data of CH 4/air flame are interpreted, and a full map of the temperature and gas density in the flame is produced. A comparison between moire deflectometry and related techniques is given.

Measurement of temperature distributions in a methane-air flame by moire deflectometry

The temperature mapping of an axially symmetric premixed methane-air flame was determinedby moire deflectometry. From the analysis of the moire data detailed information on the temperature distribution is obtained. The radial profile of the temperature shows a minimum at the center of the flame which gradually disappears when proceeding down-stream, as expected. The main advantage of moire deflectometry over other techniques is that the temperature distribution of the entire flame is obtained with no need for a three dimensional scanning. We have shown that the technique provides valuable and detailed information which could lead to a better understanding of combustion mechanisms. The limitations of the method are discussed.

Phase-locked moiré fringe analysis for automated contouring of diffuse surfaces

Phase-locked moiré systems have the advantage of rapid data acquisition and accuracy of better than one twentieth of the fringe spacing. In conventional moire systems data acquisition is performed by making a photographic plate and taking measurements from the plate either visually or with a microdensitometer. This is slow, and the accuracy is about one-quarter of the fringe spacing. The phase-locked system is more accurate and permits a more favorable trade-off between accuracy and working depth. The equations governing moire contouring are examined, and the theory of phase-locked moire fringe analysis is presented. The design and operation of the phase-locked moire contouring system are described, and the results of measurements made with the instrument are presented.

Wave propagation in layered model due to point-source loading in low-impedance medium

Dynamic photoelastic and moire techniques were used to study the incident, reflected and refracted waves in a layered model. The model, consisting of two birefringent layers with an impedance ratio of approximately 2∶1, was subjected to point-source explosive loading in the low-impedance medium. The isochromatic and moire-fringe patterns were photographed with a Cranz-Schardin multiplespark camera operating at a rate of 200,000 frames per second. Propagation and attenuation characteristics of waves in both layers were studied. The formation of head-waves at the interface was clearly evident. Stress determinations were made in some instances using photoelastic and moire data.

Moiré interferometry with embedded grids-effect of optical refraction

Optical refraction resulting from refractive index gradients in nonhomogeneously stressed models is investigated as a limitation on the usefulness of moire interferometry employing embedded grids. Apparent displacements caused by internal refraction are estimated for static and dynamic cases; Boussinesq's problem, and the problem of a spherically expanding pulse, respectively. Refraction effects are found to be far larger in the dynamic case. Moire observations of motions in models loaded by pellet impact are compared with independently measured motion histories. Anomalies in the moire data are found to agree fairly well with predicted refraction effects for a spherically expanding pulse. It is concluded that optical refraction effects are potentially quite detrimental to observation of transient internal motions using moire interferometry.

Finite rotation and strain measurement using the moiré technique

The moire-interference technique for obtaining the two-dimensional displacement field is well known. However, interpretation of the interference fringes to obtain a measure of finite rotation and a tensorial description of finite strain has not been given. This paper presents the analysis for obtaining large rotation and strain within the vicinity of a material point from data contained in moire photographs of displacement fields. No approximations are made limiting the magnitude of rotation or strain. The Eulerian state of strain obtained from moire data is related to the Lagrangian description.

The grid-shift technique for moiré analysis of strain in solid propellants

Moire principles and procedures were surveyed with a view toward adaptation to measurement of complex strain distribution in solid propellants. Compliant coating and photosensitive materials were selected for grid reproduction. The most flexible of the several possible procedures for recording moire data was found to be grid photography. A novel “grid-shift” technique employing coarse grids was developed for point-by-point determination of surface displacement derivatives, and the grid-shift relations for large strain and large rotation were derived. The technique is extremely versatile, permitting the analysis of strain of dynamically deformed specimens in nonambient environmental conditions of temperature, pressure or atmosphere. The utility of the technique was demonstrated by application to static and dynamic problems.

Thermal stresses at high temperatures in stainless-steel rings by the moiré method

The research presented in this paper is a continuation of previous work published by one of the authors. Improvements in the techniques of recording and processing moire data in thermal-strain fields have extended the maximum temperature at which useful information can be obtained from 400 to 1600° F.

Basic optical law in the interpretation of moiré patterns applied to the analysis of strains—Part 2

The object of Part 2 of this paper is to show applications of the displacement-light-intensity law derived in Part 1. A photoreading device is described, which combined with the new theory, yields an accuracy beyond the limits so far obtained by the usual method of handling moire data. Three tests are presented: one test is used as an illustration of the applied procedures, the other two for comparison with theoretical results. These tests show that the theory is useful and that strains can be obtained with an accuracy impossible to achieve by the discrete point method of analysis. Relatively coarse grids of 300 lines/in. are used for these tests.