Bending beam apparatus

When two material layers adhere to one another and one layer differentially expands or contracts relative to the other, the layers bend in order to minimize the strain energy. Subject to various constraints, such as locally uniform layer thicknesses, and that the stiffest layer be linear elastic, the local bending can be described by the arc of a circle of radius, R. If the constraints are valid across an entire sample, the entire sample will indeed bow in the form of an arc of a circle. This is the operating principle of the bending beam apparatus and is illustrated in Figure 1. 

Typical procedures of the bending beam experiments were as follows. Resin coatings were applied to one side of a clean quartz strip by spin-coating from an appropriate solvent at 2000 to 8000 rpm for about 30 seconds. Coatings were then evaluated for uniformity, and acceptable beams were then inserted into the bending beam apparatus. Stress measurements were taken during temperature ramps and holds. The specific cure schedule followed for each material depended on the manufacturers recommendations or the results of microdielectric cure studies (lfi.). Upon completion of all stress experiments, the beam was removed and the film thickness measured by an Alphastep profilometer. The quartz beams were 82 2 pm thick,... 

PMDA-QDA and BCB. Stresses induced during processing of a PMDA-ODA polyimide (pyromellitic acid dianhydride -oxydiamine, Dupont Pyralin 2545) and a bis-benzocyclobutene (BCB, Dow proprietary) were studied using the bending beam apparatus. Both materials were used as supplied by the manufacturer the PMDA-ODA solvated in n-methyl pyrrolidinone and the BCB in xylene. Final coating thicknesses, as measured by profilometry, were 2.8 xm for the PMDA-ODA and 3.2 xm for the BCB on fused quartz strips. 

Bending beam apparatus advantages for stress measurement, 358-359 description, 359 experimental procedures, 359 operating principle, 358,360/ schematic representation, 359,360/... 

Wilcock, J. D. and Campbell, D. S. (1969), A sensitive bending beam apparatus for measuring the stress and evaporated thin films. Thin Solid Films 3, 3-12. 

Thermal Stress Determination. The method selected to determine the thermal stress developed at the epoxy-aluminum interface was the bending beam technique utilized by Dannenberg (9), Shimbo, et al. (10) and others (12-13,17). The exact apparatus configuration is that of Dannenberg s except that thicker coatings were applied to the beam. 

Bending beam theory calculation of elastic modulus, 361-362 calculation of glass temperature, 362 calculation of thermal expansion coefficient, 362 layer stress determination, 361 Benzophenone-3,3, 4,4 -tetracarboxydi-anhydride-oxydianiline-m-phenylenediamine (BTDA-ODA-MPDA) polyimide, properties, 115-116 Bilayer beam analysis schematic representation of apparatus, 346,348/ thermal stress, 346 Binary mixtures of polyamic acids curing, 116-124 exchange reactions, 115 Bis(benzocyclobutenes) heat evolved during polymerization vs. 

Schematic representation of an apparatus for the determination of mechanical film stresses using the bending beam technique with optical detection [150].

We perform flexural testing on polymer rods or beams in the same basic apparatus that we use for tensile or compressive testing. Figure 8.6 illustrates two of the most common flexural testing configurations. In two-point bending, shown in Fig. 8,6 a), we clamp the sample by one end and apply a flexural load to the other. In three-point bending, shown in Fig. 8.6 b), we place the sample across two parallel supports and apply a flexural load to its center. 

BENDING OF A BEAM. The complex dynamic Young s modulus can be determined from the forced, non-resonant oscillations of a single or double cantilever beam. The apparatus considered in this paper is the Dynamic Mechanical Thermal Analyzer (DMTA) (6), manufactured by Polymer Laboratories, Inc. Figure 3 shows the experimental setup for the single cantilever measurement. A thin sample is clamped at both ends. One end is attached to a calibrated shaker through a drive shaft. 

Use was made of a piezoresistive strain gauge array to measure the stress distribution on the surface of the die. A beam bending apparatus was used to study the importance of the thermoviscoelastic properties of the molding compound. The strain gauge allowed for the study of the effects of thermal shock testing. 

The largest stresses are observed as shear stresses at the corners of the die at the lowest temperature. Three commercially available epoxy-based molding compounds were studied. Two of these materials are standard packaging formulations for smaller devices. Both strain gauge and beam bending experiments showed comparable stress levels with these two materials. The third material is a rubber modified, low stress material. As expected, stress levels in devices packaged with this material, as well as stresses observed in the beam bending apparatus, were considerably lower than those for the other two materials. 

The authors are thankful to D.S. Soane and R.W. Biernath, UC Berkeley, CA, for the use of their beam bending apparatus. 

The main part of a four-point bending apparatus together with the free translation and rotation principle of the beam is shown in Figure 7.7. 

Fig. 4.13 shows the experimental setup for validating the sensing model. A custom-built apparatus based on a crank-slider mechanism was used to generate periodic mechanical stimulus in the frequency range of 1 - 20 Hz. The mechanism converted the rotary motion generated by a DC motor (GM8724S009, Pittman) into the linear, oscillatory motion of the slider. The free end of a cantilevered beam was inserted into a slit on the slider and thus was subjected to the periodic bending stimulus. 

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