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Transcript
1. Modeling Stresses in a Leadless Chip Resistor Solder Joint There have been numerous articles confirming the primary failure mechanism for leadless chip resistors is thermo-mechanical fatigue and creep. The performance of the resistor hence the electronic assembly is dependent on the reliability of the solder joint to maintain an electrical connection. As discussed the failure mechanism of the solder joint is complex. Finite element analysis is used extensively in the industry to determine the fatigue damage and creep behavior in solder joints. Methodology In this study ANSYS APDL is the finite element software used to determine the stress and strain in a leadless chip resistor solder joint. ANSYS APDL is a commercially available software package. The leadless chip resistor is a size R1505 resistor. The device dimensions and the nominal solder joint geometry are shown in Table XX figure XXX. Leadless Chip Resistor R1505 Dimensions Symbol Description hr Height, resistor lr Length, resistor wr Width, resistor hs Height, solder joint fillet ts Thickness, solder joint fillet ws Width, solder joint fillet ht Height, resistor termination lt Length, resistor termination wt Width, resistor termination tp Thickness, PCB pad lp Length, PCB pad wp Width, PCB pad tb Thickness, substrate/PCB lb Length, substrate/PCB wb Width, substrate/PCB gp Gap between pads * Case 1: ts = .002, hs = .026 Case 2: ts = .001, hs = .025 Case 3: ts = .004. hs = .028 Dimension (in) .024 .155 .050 .024* .002* .050 .024 .015 .050 .0012 .0475 .060 .063 .310 .310 .105 From the geometry shown a three dimensional model of the device is created using Unigraphics. By establishing symmetry boundary conditions a quarter model can be used in the analysis and provide accurate results. INSERT FEA MODEL OF QUARTER SIZE A cyclic thermal load condition is imposed in the analysis. The temperature will vary from -40OC to 125OC (-40OF to 257OF). The transition rate from the minimum to maximum temperature is 10OC per minute and a 20 minute dwell at the temperature extremes. The thermal cycle profile is shown in Figure XXX. The purpose of thermal cycle load is to induce plastic work due to the mismatch in the materials coefficients of thermal expansion. Thermal Cycle Profile In this analysis the resistor, resistor termination, and PCB pad are represented as isotropic linear elastic solids. The substrate (PCB) is represented as an orthotropic linear elastic solid and the solder is considered a visco-plastic material. The material properties used in the analysis are shown in Table XX. Material Properties Resistor Resistor Termination Ceramic Young’s Modulus, E (psi) 3.5E6 AgSnCu 1.2E7 - 0.37 18.9E-6 Substrate (PCB) Epoxy (GFG) with Cu layers (Ex) 2.5E6 (Ey) 1.0E6 (Ez) 2.5E6 18.7E6 3.6E6 (GxY) 0.4E6 (Gxz) 0.5E6 (Gyz) 0.4E6 - (Nuxy) 0.26 (Nuxz) 0.14 (Nuyz) 0.26 0.35 0.39 (x) 18E-6 (y) 70E-6 (z) 18E-6 17.5E-6 23.4E-6 Description Material PCB Pad Cu Solder Sn63Pb37 Gravity (g) = 386.4 in/sec2 Shear Modulus, G (psi) - Poisson’s Ratio, Coefficient of Thermal Expansion (1/OC) 0.25 40E-6 Governing Equation: The Anand Model In ANSYS there are various models available to simulate visco-plasticity. The Anand model was originally developed for metal forming applications. It is however applicable to applications that involve strain and temperature effect including solder joints and high temperature creep [ANSYS]. The Anand model does not require and explicit yield condition and loading /unloading criteria. It assumes that plastic flow occurs at all non-zero stress values. The Anand model represents the non-linear rate dependent stress-strain relation of solder. The model uses a single scalar internal variable (s), called the deformation resistance that corresponds to the isotropic resistance of the solder to plastic flow. The deformation resistance (s) is an average resistance and represents the resistance of the plastic flow from such deformation mechanisms as dislocation density, solid solution hardening and grain size effects [Anand article]. Therefore the deformation resistance (s) can be considered proportional to the equivalent stress. σ = c s; c < 1 And C is defined as: m 1 Q 1 p c sinh exp RT A Where p is the plastic strain rate, A is the pre-exponential factor, Q the activation energy, m is the strain rate sensitivity, is the stress multiplier, R is the universal gas constant, and T is the absolute temperature. Rearranging the equation to have the strain rate a function of stress and deformation resistance the equation is re-written as: 1m Q p A exp sinh RT s From the above equation p Q s sˆ exp RT A Where s* the saturation value of s, ŝ is the coefficient for deformation resistance saturation value and n the strain rate sensitivity. From the development of the above equations there are nine material parameters that need to be defined in the Anand model. n * Solder (Sn63Pb37) Constants for Anand (viscoplasticity) model Constant Description Value Unit so Initial value of deformation resistance 1800 Stress (psi) Activation energy / Universal gas energy/volume/ Q/R 9400 constant energy/volume temperature (OK) A Pre-exponential factor 4E6 1 / time (1/sec) Stress multiplier 1.5 Dimensionless m Strain rate sensitivity of stress 0.303 Dimensionless Ho Hardening / softening constant 2E5 Dimensionless Ŝ n a Coefficient of deformation resistance saturation value Strain rate sensitivity of saturation (deformation resistance) value Strain rate sensitivity of hardening or softening 2000 Dimensionless 0.07 Dimensionless 1.3 Dimensionless USE POWER PROFILE IF ABLE TO GET MODEL TO RUN The finite element model is composed of a single element type (ANSYS Solid 186). The Solid 186 element is 3-D quad 20 node element with three degrees of freedom on each node: translation in the x, y and z directions. The element supports plasticity, hyperelasticity, creep, stress stiffening, large deflections and large strain. The Solid 186 can also be defined as a 3-D tetrahedral 20 node element that makes it highly suited to modeling the irregular geometry of the solder joint fillet.