tokens: of the neck radius, a , determined by the numerical simulation and laboratory experiments. The spring constant increased almost linearly with neck radius, and the results from the numerical simulation (circles) and laboratory experiments (triangles and squares) were observed to overlap. Figure 6. Results of FEM simulation (circles) and laboratory experiments (triangles and cubes) for compression. The solid line denotes the semianalytical formula (Equation ( 4 )). Triangles and cubes are determined using the data between 90 to 95 and 40 to 90 N, respectively. The error bars of laboratory experiments are the standard deviation of three samples. The upper curve is from SU17 . The inverse triangle is the FEM simulation result for the a = R cylinder (without shrinkage due to sintering). Two sets of laboratory experiment results are shown in Figure 6 ; the difference between these sets is the force range used to determine the spring constant. Figure 7 displays the applied force as a function of displacement as measured in the laboratory experiment. This relationship was not linear, particularly for small forces; thus, the spring constant is dependent on the range of the applied force. In contrast, the FEM simulation was based on a linear response. The spring constant at the commencement of the compression was small compared to that at a large compressive force. There are two possible causes for this nonlinear behavior. First, the misalignment of the two end planes led to a nonlinear behavior because the force required to enable deformation until perfect fitting to the autograph was small compared to the force required after the perfect fitting. Second, if there is a bump on the end surface, the compression force changes at the commencement of compression. Figure 7. An example of a laboratory experiment result. At the beginning, the force increases nonlinearly, and then increases almost linearly after reaching 20 N. The neck shape was adopted from the second curve from the bottom in Figure 2 . The spring constant was determined using the data in the linear region of the force-displacement curve. For comparison, two ranges of the compression force were used; 40–90 and 90–95 N. Although there was a considerable scatter in the data, the results from the laboratory experiments were consistent with the numerical simulation results. The maximum radius in Figure 6 is 2.375 mm, corresponding to the original radius of the sphere prior to sintering. However, this radius was not realized by sintering, because the volume of the sphere decreased as a result of sintering. The maximum radius () following sintering was . The solid curve in Figure 6 is the model in SU17 . In contrast to the experimental and numerical results, the spring constant of the model increased as the neck radius decreased. In this model, the deformable region was restricted to the neck between the spheres, and the length of the neck decreased with the neck radius. As a result, the
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