2.1 Anand constitutive equation and parameter fitting
The Anand model is a viscoplastic model of metal thermal work proposed by Anand and Brown [4]. Suitable for describing large viscoplasticity and small elastic deformation. The relationship between the saturation stress and the strain rate of the viscoplastic Anand model is as follows:
![](data:image/png;base64,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)
The relationship between stress and strain at different temperature and strain rates:
![](data:image/png;base64,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)
The above equation contains the nine parameters of the Anand constitutive equation:
According to the formula derivation, they are constant, activation energy / gas constant, stress multiplier, saturation value coefficient of deformation impedance, strain rate sensitivity, strain rate sensitivity index, strain hardening parameter, strengthening coefficient, and initial value of deformation impedance. The parameters of the constitutive equation model of nano-silver are calculated through formula deduction, which are listed in Table 1 [5].
![](data:image/png;base64,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)
2.2 ANSYS finite element model
In order to facilitate the study of thermal fatigue effects of solder joints, the model needs to be simplified. Due to the symmetry, a quarter of the chip can be used as the research object, which contains 12 solder joints. The model is shown in Figure 2. The material parameters of each component are listed in Table 2 and Table 3 [6].
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAvEAAAE5CAIAAACWCejyAAAAA3NCSVQICAjb4U/gAAAACXBIWXMAABYlAAAWJQFJUiTwAAAgAElEQVR4nOy9/4vbVtb4f/xhf92msvNTn3QolgsbkmVKIycP3ZmFBhK5QyktTbHTDSXQkKmcUmiezUxrp5QlyWzt7Rco7dgOCYTSJ5ZJwpby2B0n0IHYlE3qFBsaUuhIhDbkJ2mcpH+APj8c5r5vJVsjzzfbynn9MIylq/vl3G9H955zFbAsCwiCIAiCIIac/6/fGSAIgiAIglgDSKchCIIgCMIPkE5DEARBEIQfIJ2GIAiCIAg/QDoNQRAEQRB+gHQagiAIgiD8AOk0BEEQBEH4AdJpCIIgCILwA6TTEARBEAThB0inIQiCIAjCD5BOQ2w09Xo9kUjEYrF+Z2SD0HU9GAym02kvgVVVjcVi/hNOpVIJBAKVSmXjkzZNM51OB4PBQCAQjUbXOw+6rmez2UgkUq/X1zUhgiCckE5D9Ew2mw0sR7dn6/X6zZs3S6VSTynqup5IJDDmWCzm19miUqn88ssv1Wq13xnxFbFYbGRkZHFxsVartdvtL774Yl2Tu379+unTpzVNW9dUCILojEUQPZLJZDKZjGEY+FOWZQCo1Wr4s1arCYLgHgMAyLLsMTnDMARBiMfjmUwmHo9juy2XyyvOf68oirJhaVk9CmdgKRaLrEn0kXK5DACapm1koplMhu8RhEc0TctkMv3OBTHc0DoN0TMjIyNTU1OhUKjj3bGxsX/+859rmNzZs2dnZ2dVVZ2amlJVNZ/PA8Bbb721hkm4oOt6LpfbmLT8xPHjx/udBQCAH3/8EQDC4XC/M0Isz4cfftjvLBBDD+k0RM8kEgn3AJOTk2uY3KZNm/gUJycnRVHcmLV90zTZyhDhnWQySZsvRE+oqkovD8TqIZ2GWBdM00wmk2iYGQwGk8mkaZrOMGglE4lEVFXtFpVTQ4pEIoIgdEtXVdVoNJrNZpkVTiQSabVaAKCqaiQSQaMcPj9o1In2OolEAgPrur5r165GowEAvJEQXzTe5pQ3Dk2n04FAAO2CVVW12URXKpVoNIpx9mS1qut6oVDAJCqVCisLZhgAWq0W5s00zVgsxpvlskSxOnRd9xinTUSRSCSbzboUORaL4eQ0Pj4eCATq9bppmoVCAStl2TixFJjVSCSSSCRsT9mwRcKqFa2+pqenWfV1i6fVajFrLVb7tsidtwAAWxqKNJ1OO1s4k2cymXQpgntUtvbG9xRW3QCAlchaHetcwWCQPdJqtdBcGouGcTr7ZjeR6rqeTqdtTcVWtG69o16vs6xi0sFgsFAosBT3798PANPT0y41RRDL0+/NL2LosdnTIPF4HFdTrCXzgnw+z+4CgCRJaCKjKAo2xWKx6DFFSZK62bjUajWMMB6PK4pSq9WKxSIAiKJYLBZTqRQLkEql8BHczML812o1fNZWOvbTMAxJkrAsmqZJksSeLZfL+FOWZUVRBEGQZblWq2HxmYlMs9kEALQb0DRNFEWb+RF0t6cpl8u4bpRKpWRZzmQymKIoioZhaJpWLpdR28Pis4QymYwgCKyMgiAIgoC14x4npqsoiqIohmEYhsFH27HIlsOghCXBW0t0i9OyLEEQsDHUajVRFF1sLGRZliQJC4L1KEkSHwBz0u1xrA5RFG2SwYK7N4xUKsWSxlRYm2Q/M5kMa298+7fhEhUak9kEhU2Xr+5UKoUGTNhc8/m8oijFYpEFwOaB8sTwmD3WWryItFwu4+Pditatd2BWsZuzrOLdZrOJz6KEyZ6GWCWk0xCrpaNOI8syP1Daxk3blInD2bKWxQhuarhYfWJsTGWxLAtHXt6smNcbcGTnc277yU+KqITZ0uKjYkO8pmmsgHwYfIQN5fgI+2ktZyNsm/Msy8K5gc0rmGGMEP+ixHiVEfU8W7a7xYkTIZ8H/nWoY5GdRrK2GcslTgzJRFcul7vNc1gKviXYdCPLg04jyzIvGQzPK4J8SPYTM8kKqGkamrHzkbD2ZhiGrf3zuEelKIpNUKhVsPBY3UxcWNe8YmerCwzPiozJsQazrEg7Fo1vSC69w5ZV1HL4JkE6DbF6aO+JWBfm5uZwxRsX1QHg3r17fIBIJMKsjMfGxuLxeLvdtq3tdySVSuXz+WWtPjdt2sT+f+KJJwDgkUce6RhyampqcXERlg7OqVar7Xa7W7QXLlzI5XLMZX18fBwAbN7X27ZtA4BwONzRjHpsbMyyrNHRUV3Xk8nkBx98AAC//fabe3FsvPrqq+z/f/zjHwAwPz/PBxgdHWV/z549CwBbt25ldxOJhCAI1WqV7UC5xPnNN99omuZ01Oc96t2L7MQlTsznkSNHMG8TExPdIvnoo48EQeBbAm5Tnj592kseAMA0zWq1un//fpYN3Kv69ttvwbVhnD9/HgDGxsbwZzgcXlxctO2fsvaGMrG1f4ZLVKZp5nI51C8Zx44dY08xmNhRGsvWAjNQC4fDqLX85z//Ac8itRWN4aV3sEe69UeCWA2k0xDrBe64X7169cyZM8sGfvrpp8HD1K6qajAYXFsbZABotVqxWOzkyZOvvfYavk12o9FodHyV7Ck5tDnYu3fvX//6V7b1tmJ27doF3adMALhx4wYAbNmyhb+4c+dOALh79+6ycd64caPjuhGbhleAS5yhUKhcLl++fFkURbT7mZqa6hhJo9HARQsG6nDezZNv3boFnZyu5+bmMEC3hsHrgqvEJSrMnq2MqD6uYQb+8pe/AMD9+/dh1SJdk95BEKuBdBpiXUin0wcOHLh06dLs7CwOi6un1WqdO3dudnZ2TWJjVCqVp5566uDBg3Nzcy6rAozbt2+vJjld15988kkAWFhYSCQS/HrSyvC4NIIT5MriXFhY6C1PHnCJc2Ji4ueff85kMqqqiqLoYj+OFtyr5M6dOx2v99ow1glUSdcP23rJKkW6yt5BEKuEdBpi7dF1fWZmRlEU79rM7du3BUFwefVvtVrT09P/+7//u0Z5/H+89dZbkiQt66COSJKkqqrNT4S5b3jhww8/bLfbJ06c6C2X3cFX9h07dnQLgFsJN2/edN7qJnA+zh07dmiaZju7uVKprGapYNk4Q6HQ1NTUzz//LEnS/v37nS5FsLSA4dyvdF9p48F9rnPnztmuY4W6NAwUqc1hzUX3csElqsceewwArl+/7nxq9+7dK0irI6jSbd++HVYt0tX3DoJYJaTTEGuPbUej44RkC6CqKr8Lgw7A7CdTaPj1g7UaK23r6u65feWVV9rtdiwWY7NvvV73YgbEsKkCuObfKw8ePGD/45z3+uuvdwuMhjL/+te/+IsLCwu2ba9ucT733HMA8MILLzAVRNf1Tz/9dDUH2bnEWa/XmXIQCoXQsqfjUsrhw4fh980AZXvw4EF2BZcNutVpKBSSZblarfL+zNlsFhfPXBrG888/DwBvvfUWu2ia5tWrVz0Wn8clqnA4LMtyu93mtSUUxb59+1aQFoMvy9WrV0VRxIUoLyJ1YfW9gyBWy0oMiwliCfRMht+7qqI3BHrkFotF9ONFJ090r0CP2Xw+jy6mkiRJksQcItCDlLl+NJtNQRBSqVSGw+auwmN73LIszADv64HZQ/8OtMHMZDLocoyvquVyGcPjG2q5XE6lUujXw2w20euVuf4ahuH0WLaWHDqYn1cqlcLsoSss8zDCp2yBnaDjiSRJvPsxc/JC53Bw2IhgorxLMC9w9zitJecXDMO7uXUrMvMewgbArvCV0i1OTB2fwvht7tk8vH8WNiTe78YwDJSGix81ti5sD7Isi6LIDH3cGwYWHF3NU6mUKIrYtg3DYA7VLAn3Ou0WlbXkl2Tzw2ctmRWQhce0+Mq1nVyAeYvH47y3Nu8S6C5Sm9uUrWjuvQPlzJyqbP2Uecu7eLoRxLKQTkOsHOeKNJtKi8UijsU4mOLoxmsVeJwJG8r5aNHJkx3C0e14vY4zhC1L1u/tE/H8FVuG8YQSHE8Nw8Dpn80BOOfZJhKWeTY3OBPCi7bkLG7OkySp2WxiYWVZNgzDmTdnAZnfNeZZFEU2d+KswLBJNZ/P4yPsvBMvcfJh8C5TfboV2eLmNhQjXyl8sI5x4sklrNJtWbWB9dWxIdmE2U2elmU1m03UKrC5suTcG4ZlWSzpeDzOtAr39tatIB2jQjRNY4dZS5LE9A9ndTvbj7OCsC5YcrzklxWpe9GYmuvsHc6sOvuptaR+YV/oJiiCcCdgkVE6QQwP2Wx2enq6Vqutxu1oA+IkBpNYLFatVmnYJ/wK2dMQBEEQBOEHSKchiGHihx9+gC5OTAMVJzGAmKaJLvRkt0v4Fdp7IoihgZ23CwCyLLOj4QYtTmIAqdfreLAvkslkuh1mSBDDC+k0BEEQBEH4Adp7IgiCIAjCD5BOQxAEQRCEHyCdhiAIgiAIP/CHPqbNGycSBEEQBDGkDIhtbj91GhgYKRBDQSBAJu0+gapyPSCpEv1icFYoaO+JIAiCIAg/QDoNQRAEQRB+gHQagiAIgiD8AOk0BEEQBEH4AdJpesY0zWw2G4lE6vU6XtF1PRgMptPp/maMIAgb6XQ6GAzqut7vjAwTuq7bhriBQtd1rNbBzN5A8RC2/4HWabLZbOD3ZLPZfmcKzp49e+HCBU3T+p0Rwk4sFrM1GH7U46/HYrE+5hOJxWKRSKTfuRhQnFUZCASi0Wg6nTZNs9+588qgVXG9XndK1dllrl+/fvr06cEc4kzTvH79eqlUarfb/c4LMZBY/cNL6oZhyLIMALIsG4axAbnyQiaTAYBarbZO8SuKsk4xDzXLNhjDMPL5PDbseDxuazDYlgRBKBaL65lNrwiCAACD06o3Eo99XxRFACiXy5ZlaZqmKAoAiKI4LELb4CpeVqq1Wi0ej2uahj9xHMtkMvhT0zRJknBYW+8hbpUMePYeQvqrS/AM9DoNAIRCod27dwPA7t27Q6FQv7OzEei6nsvl+p2LoSQUCk1OTqZSKQDQNM3WYPDnl19+mUgk+pO/37Nz505YyhXhJBQK4SLHI488AgDhcHh2dlaWZU3T3nvvvX7nzhMDWMUzMzPhcLjjrXA4fObMmQ3OD0GsLYOu0zxsmKYZj8f7nYvh5tSpU5IkNRoN205loVDYsWPHxMREvzJmY8eOHbgGSXgH33BUVe13RjwxaFU8NjbWTaFBRkdHx8bGNiw/BLHmDJ9OY5pmoVCIRqPZbLbVauG+eywWs5lBFQqFSCTiNMcxTVNVVXxcVdVgMBiNRvGRVquVSCQwZCKRaLVafIRoNBcIBCKRyA8//MDfUlU1kUjYTDQqlUo0Gg0EAsFgMJlMohGAe+Z1Xd+1a1ej0YAl4491kN9DQalUEgRhenqaVaKu62fOnDl69KgzMF+z2ELg95YHLJjNFofVu2mayWQSY7DZLdbrdWwGTmuekZGRHTt2YDDTNLHtBYPBRCIxICtJQ4Gt2/LyR2NSvlJc5IzWlFg7bExAOrYQW/yVSgXDJJNJ9iBfxe5JDCwdywUA2OaxONFotFKp4HXevjidTgcCgXQ6zV9kPQI7DnBi4d0s+Pj5IbTvdJwmbKafwBmE4ZtVq9XCYmJgLJetUKyZ2Sager2OomDPBoPBQqHAHuzWqp3tHxwVx78eLJvQcNDHfS+Pqds2fXFLGADi8biiKLVaDU0o4vG47RHcbS0WiwAgCAJ7HHflZVmOx+O4YW9ZVrPZFEURH6nVaoIgCILANsIVRREEAe8yiw0WGJOTZZlloFgsSpKE+9YYHu96yTy+2K1UqH6mJ7FgvTPbC0mSms2mM5gsy7aakiQJbzF7Dha4XC6zqmw2m1jvkiQpilIul8vlMjYbFr5Wq7Gm22w20bqCZQNrH//H9mBZlqZpsizzbcmXeKxK7Au82QTrPvgTJYxiRHMQWLK/MQyjXC5jDbIYusk5n89LkmQYhmEYuHfJ56FbC2HxK4qSyWTY2MKqla9ilyTWil7jtA2tzlvdymUYhiRJNrGjkMvlMv6UZRmHTVmW2UUWIUpAUZRUKpXP52u1Gl93lmXh4Ixix8yw1K3+2dO4TBP4k29+fMus1WrYVFKpFAoBA7OWjE2LxcxuaZqGww4+WywWmazYSNKxVXds/4ZhCIKgKAq2Q6zWVCrlMSEXBmfOGj6dxlqqcqwJBEXPfmJHYj9xHGT1yrcYwzCw28iyzJuO8oliTfP9B5sCf4XXabDdMEM86/dD87KZJ52mG72KBes9lUplMpmOAzfqPXxNYc2ywM66sCmv/AxnWRaO1PwMyj+Ow1bHnPCjOdoy91TSoaMnnQY7pmEY2CsFQWCDrCiKvEE9uurwbyO2ya+bnGVZtnVJ/GfZFoLx83HaWghflo5JrCFrrtPYysUm4Ewmw4sdxzRWal4F0TQN68IWoWVZON2ymuJfACzLwndOvmjd3lo3EpdpwlqaKVBzVRTF5ovAN2bLsjRN419yUMvhA9t+8rLChFi6LqOHTVCKooiiyOfKpvS4J+TC4MxZw7f3xNi0aRP732aFZ3Pze/rpp52P48VQKBQOh03TrFar+/fvZ4uH09PTAPDtt98CwBdffAEA/DbzE0884ZKxa9eutdttURRZbNVqFQC+++47L5kn1orPP/9cFMWZmZkLFy5MTU05A3z00UeCIPAWBpOTkwBw+vRp76nw1cdXKwDcu3eP/7lt27ZukUiS9P777+MSMbOLJ5CPPvooGAxu3rx5eno6Ho/Pz8+Pjo4CQKVS0TQN/0fC4XA8Hm+321euXOkYVTc579ixI5fLsXX4V155hSXtpYWgFTO49uVuSQwytnKx9nzhwoVcLsfGt/HxcQDAUY6BrT0cDvMyYRECABqAd5PY3NwcygpNBcDRmzYe92kCACYmJlKpVKPR2LVr1xNPPNFxB5ldDIfDqB//5z//AYCpqanFxUUAqNfriUSiWq06ndWZrHgxgufRwzTNXC6Hr9CMY8eOAcD58+e9JDQUDLFO44IoigsLC+zn/fv3AeCxxx7rFv7WrVvQSeufm5sDgFKp1JOh348//gidlNaO0yqxfoRCocOHD0P3+aPRaOBrCgMnyLU6mQPnQmbp9eDBAwAYGRlxhkR/k/Hx8VgsVq/XqanwfPLJJ4uLi9iJVFVlSgx2tMcff5wPjO8qv/zyS8eousn56NGje/fu3b9/fyQSUVWVXV/DFtItiWGk0Wh0W25cQ9CU5+rVqwPijeU+TSDooKBp2jPPPLNshH/5y19gaXoCALSwPHny5GuvvdbTjONx9MD829ozqp5+OpTPnzrNp59+uri4yIyzcrlcKpVyN/gHgDt37nS7xWtIHvFTK/ExaJG9Tvz9738XRTGVSpmmaZrm+++/L0lSx7e30dHR77//vlgsLiwsjI+P2+wxCRdQs/FINzmHQiFVVWu1WiQS2b9/fzQaZcaba9VCXJIYRm7fvr2u8afT6QMHDly6dGl2dpZfius7LtMEAJimGQqFBEF44YUXlq1ffhWkUqk89dRTBw8enJub69U3s6fR48aNGz1FPnT4U6eZmJhIJBIXLlwIBALPPvvsO++8c+rUKZfwW7duBYBz587ZrqPJNxrHeB+Atm/fDgAXL17kL6K/lecSEBsBvrLYHNwAYK38b8Ph8LFjx+7du7d58+bNmzdHo1H+lc5JIpFYWFhQFCWXyzFHEqIbuOJlc0JE3N+Su8l5bGxsbm6uWCw2Go2PP/4Y1qGFOJMYRiRJUlXVNiSuoYOMruszMzOKogyUNuM+TSBHjhzJZDKzs7PtdvvIkSPuEaJ6hPPFW2+91e2FxyPLjh64U3H9+nXnLT9tdvtTp0mn04IgfP/995ZlLS4uLrvMGwqFZFmuVqu8c102m0XzCGxn3o/52rVrFzoSs7ZumuaRI0fwAC5icMCdKX5IwtW1gwcP4k/s6mzJzTm3uVOpVM6cOTM3N4dr1LOzs92sB/hXqxMnTgDAr7/+2lNaDyF79uwRBKFUKvFrordv3xZFsdshK93kzF9PJBK4fQAeWoh3uiUxjLzyyivtdps/QaNer/faO1y4e/cu/3NAFrTcpwkASKfTL7744ujoaCKRSKVSpVLJqefxZbl69aooirgqY2sMPRXZ4+gRDodlWW632/zbNepV+/bt857coLNKG+PV4CV19m0E/qh75mfIwuDrFPOGAAB0fULQ7cV2Irjt7HzmaosPiqLIrMeZgXo8Hq/VasVikTlworU5WuzzR7ajuwReRAt2m6OES+axvOVyOZVK8Q4XRK/N1cuHNdBijvdK5R06sB6x3jOZDHoBYG0ahoH1jm4OGB4dnZjTKUsdQQ+sjs4aAIBxWkseEP6uei9VqWka62jdwjBPE+ZrzXtFWUtVwGqkm5zRywb/x2pljiTuLcTmzNJsNqHL1xtcklgreuogbOTh/YnYLZvcbOVCX24c4tDXnfmaGYaBvcBmcGPrGix11s6xr2FXRTcr/IxJsVjEZ9F7HCvXlr0Nw2WaQF99FpLpKKxtsImMPxfA1sxwkGGHjJTL5WKxiI60vKxsJ4C4jB42QeFcxs4lQf9zlsNlE3Khv7oEz0DrNDj982QyGduqL44OfADLsvL5vCiKWD22wLbH+eSazSZ2HkEQUqmUTePBB3E+y2QykiRhU7Blkj3CjmQQRdE2yblnHrvN4HyWaHDoqdt0bDzOYHhYCDYVURSdYdA9WxRFrA5sAJqm2eK3VSU7w0YQBJtRXseciKLIgsmy7OVAiKFm2ap0bu50c9xlp2gAQDwe50XnlHk3OcfjcRaJKIq8tuHSQmw17mwSfD5dklgrvHcQ997hXi4Mg+7K7GWPzYLOXuC86Bz3nMNysVjEYRAd4FFtwj7YMYkNo+M0wUTUscgoWywja0vs01osWqZishOMUqmUF1l1a9Ud61fTNHZUvSRJrB16SciFZQNsGAFrrY3VvRMIrEvquNHz+eef8+v8pmmePXsWAIba3eAhZ50azPqRTCYnJydtNgGVSuXTTz91N6zxPUNXlUMBSXWQicVi1WrVrxU0OG3Ph/Y0aHnn/H7hpk2bvPjXEcSaUKlUeMdjxn/913/5ySKPIAhicPhDvzOw9miaViqVgsHgX//61y1btgDAgwcP/u///u+vf/0rfZ6N2DB+/fVXtKN86aWX2Gl733zzDQC4e+ERBOEzTNPEA0FardZAOXP5D3/uPZ09e/bChQt4sIQgCIlE4tVXXyWFZtgZnOVNj6iqeu7cOXa+ajwef/HFF+n7lDCEVTkUkFQHk3q9jkctI5lMxn8mEIPT9nyo0xB+hRqMb6CqXA9IqkS/GJy250N7GoIgCIIgHkJIpyEIgiAIwg+QTkMQBEEQhB8gnYYgCIIgCD9AOg1B9IxpmtlsNhKJ1Ot1L+F1XU+n08Fg0GN4Yq1AsfMfhCLWlXq9Ho1GA4FAMBjE7yKZpom1EAgEotFooVAIBoPpdNpjhNFoNBqNrmueCT9BOg3hH+r1ejqdDgQCgUAgm826hIxEIoElVqBn4GEBHr9BaJrm9evXS6VSu93uNSGCGCIqlcrBgwfn5ubwywm5XO7OnTuxWGxkZGRxcbFWq7Xb7TNnzvQ7m4Sv2eBvMfD0N3Vi6PDYYNiXubp9t5J9YRQ/JbMy8Asv3T5CtPrw/mb9+r7LBy99T99HVNsHPq2lj4wOzgdZH+bmsa70ve0xaJ2G8CGiKLbb7YsXL3a8e/z4cfzk23PPPbex+SLWF1VVaZupjzQajSeeeIK/8uOPPwJAOBzuT4Z+j67ruVyu37kg1hfSaQgfcuzYMQD417/+5bxVr9cjkUgkEtnwTBHrS6vVSiaT/c4FMaCYpsm+R034GNJpCB+ybds2WZY1TVNV1Xbr5MmTx48f7/hUq9VKJBJoZJNIJJx2NmgXHAgEIpHIDz/8gBfr9TozzWHB8GcsFuuYkM2UxxkDAKiqimlFo9FYLPawGRebpqmqajQazWazqqoGg0E0FDVNM5lMosEps0IFgEql8uyzz7bb7Wq1yiSPptk2U24+hmg06mwhvkfXdV4CtqbFN/JsNoviZVQqFZsJMF5nrXd6epoZtAUCgenpaXYXTdxUVU0kEraugXWN0abTaRZtvV7HrC6bB9M0C4UCNphWqxWLxbAZ4Lqdruu7du3Cr+XYOhrhN/q479Xf1Imhw2ODkWW5VqvVajUAkCSJv9VsNvEK2tzw1i0YPp/PW5alaZokSQBQLpdZAEVRBEHAR/L5PHYf/GkYBm5mscBoRiDLMrtis6fBV0b2U9M0QRBYDM1mUxCEZrNpLVn/+MwQZ9mqrNVqiqKgDOPxOBMv/o/2GShSrDIWLZO5YRjlchkfZNIzDEMQBEVRDMNAO1ZYnVnVQOGlg2BLY+0c5cPsXWRZliQJf2Ij53tQsVi03eVbOGYgk8nwV7CO2M9arYZX+AdTqRSLFu+i1Uuz2cR+xMfQLQ+1Wg37VDweVxSlVqvh3Xg8zp7FXr+siIgVMDiCJZ2GGBp60mksy7LNZ5ZlKYpSLBatTjqNKIq8/SD6NDFDYxxbbVHxV5zDpbtO4zQZ5mPIZDL8XJJKpR42ncZa0jJxTjIMA6cxVHH4eGw/bbOsTc6KooiiyAdwNpLhxYtUZVm26RMAwGvPvD0vNnJUU1Ad5O86O9GyOg0LxvKAtWxT7rspIu55wKh4DRXfTDpGRawtgyNY2nsifMvJkyfZXwDQdf3y5csdP4tdqVQ0TRsdHWVXwuFwPB5vt9tXrlwBgC+++AIA+E+722wh15bt27c3Gg228v8w2zI//fTTABAKhdDOdG5uDneLcLcCAO7du+cxKtM0c7kcznMMNL06f/782mZ7MNF1vVqt7t69m105deqUZVnY8j/66CNBEHh73snJSQA4ffo0AFy7dq3dbouiyPZJ8YPz33333WqyhJJnPSscDi8uLnbbEPSSh02bNrH/Q6HQavJGDCOk0xC+JZFIiKJYrVZbrRYAnD17FicwJ+id8fjjj/MXcTb95ZdfAKBUKuFL3sYwMTGRyWSmp6effPLJbDa7dQtT1lgAACAASURBVOtWXp16yKlUKpFI5OrVq72edHLr1i0AwIUZxrZt2wDgIfGWunv3rsvdRqNhEw7qOrhmiX3E+Vo8NTW1miz1JPl1ygPhJ0inIfzM4cOHAaBQKJimWSqV9u3b5xIYR8xuLCwsrHHmXJmamtI0LZFIoGaDahmRTqcPHDhw6dKl2dlZfl3NOzdu3FjzXPkGtKJ1YRCUv0HIAzGwkE5D+JnXX39dEIRcLvfee+8dPny421r0yMgIADBXJp5nnnkGAHAX3+YDst6Ew+HZ2dlmswkAhw4d2sikBxNd12dmZhRFWZk289hjjwHA9evXnbf47RgfgxK4cOGC7Tru9eAijVN7xhXK7du3A4DtzCd0T1tNlnCrq1KpOPPjZJ3yQPgJ0mkIPxMKhdDOMZfLuSzS7NmzRxCEUqnEvwLevn1bFEXc9EErnPfee69bDDgpsseXXVZBVenOnTv40zRNfh0om82yqEZHRxVF8fgdBn9j2zrpVcUMh8OyLLfbbX4KxCpwX8DzDeFwWJKkRqNRKBTYRdzcBG5Rk93CRnjw4EEA2LVrlyAI09PTLIBpmkeOHNm5cycf+P79+3yKt2/fBteaev755wHgrbfeYmFM07x69WrHwMvmgSDI74kYGrw0GHRP5Z0vUBuw+TThKynvIoGeTbybKPOmtjhf63g8XqvVisUixqAoCvp7o88I3s1kMhibIAiZTAY9p/BllzkeY64kSSqXy8ViMZPJYIBUKtVsNtHvCb05MLe+8TdGvFQluszE43H2jQvDMFCqxWKxWCyi764kSfl8HmsKAERRRD9wfMQpdkEQmE9+rVbD2NalkBuOF6nish82XWx1fNdAA2r+RAP+LvuoiCiKsixj82Z30XdaFEW+vrCb8P726J3EB8N6xG6bSqVEUWT9Dh2dYMkzyz0PvB84nzp7FhtDuVxOpVKD87kGfzA4sznpNMTQsGyDsZnx8h68/AkcNrWeBavVaswpJh6Ps6EQaTab7EtSmUwG1Q5+OkS3WFEU8SIGw3T55JgXa7FYxPkV9RWcXTBRpuKw5FYtvMGi16pk121CkySJV0pwwmOTIh8Dk6Gmaew8WdQp16WE/cDjiIqnNDE1gr9lGEYqlUI1wnnXsqxyucyetZ0MZGvkqGHYOprtInucJcr3O9R+nP20Yx6cfd9Z+3jsk5+02MHBY9vbAAKWozluGIFAP1Mnhg5qML6BqnI9IKkS/WJw2h7Z0xAEQRAE4QdIpyEIgiAIwg+QTkMQBEEQhB/osz1Nv5ImCIIgCGKtGBB7mj/0N/kBkQIxFAyOGRqxSqgq1wOSKtEvBmeFgvaeCIIgCILwA6TTEARBEAThB0inIQiCIAjCD5BOQxAEQRCEHyCdhiAIgiAIP0A6DeFPVFWNRCL1et15K5vNBoPBQCAQiUQqlUqvjxMbSaFQiEQigUAgFost+7XzSqWCgYPBYDab3ZgcDh31ej0ajQYCgUAgkEwm+W/RLxs+Go1SpyAGmv58ZsqyrEH66hUxFHhsMM1mE7+qDdx37xipVAo/sKcoCnYBWxj3x4k1wWNV4qcNsRYUReG/lO6kXC6zbztj9fnv25/ueJEqfoocP8qNX4IUBMHlI9X4MUj2qUj8+Db1C8LG4MzmftBpNE1j3+m1LMswjHw+b/uoLA5z9H35oaanBoNfALYNvpqm8R8TxgG648zX8XFirfA4+9pqRxRF9lVzJ2wEsCyr2WwC9wn0hwQvUrV9cB4/Ua4oikt4mxglSYrH46vJJ+E/BkenGYK9J9M0k8kkbhZEo9FCoYBXuoW/cuXK/Py8pmkbmUliKNi0adPk5CT7uW3bNrzYvxwRXTl//jwA7Nu3j12Jx+PVarXbDtTRo0fZ/6OjowDw6KOPrnMehwzTNF988UUUDjIzMwMALttP9+7dM02TvxIKhYLB4PplkiBWw6DrNKZpPvnkk99//32j0bAs68yZM/Pz85s3b+Y7YTgcXlxcPHXqFP5MJBJvvvmmLZ5Tp04tLi6Gw+GNyzoxeIRCIf7nzZs3JUnitRxicFBVFQD4PvvnP/8ZAKrVasfwfOW2Wi1BEHDCJhihUCiRSPBXULwuyt/u3bsbjQZ7h2y1WtevX6cuQwwsff42wrJ8/PHH7XZ7bm4OB6zR0VFVVYPB4LJ2bQThgq7rH374oaqqP//8c7/zQnRA1/V2u40GH4wtW7YAwA8//ODyoGmaZ8+e/eCDD77++mt6h1kWXIN58cUXuwV4/fXXL1y4kMvldF0/fvz422+/PT8/z6/0EMRAMejrNDdu3HBe/Pvf/77xOSF8Q71eF0Uxl8u1220v3jTExnP37l1wrKsh9+7dc3lw8+bN09PT7Xb7hRde6ObURjCuXLkiiqJt8YYnFArNzc3JslytVsfHxz/55BNSaIhBZtB1mpdeegkAYrEYv6cbDod37NjBfqqqmkgkYrFYt0h0XU+n0zbXXNM0s9ksen5GIpFCocA/UqlU0H0xGAzy7o6maRYKhWg0ms1mW61WLBZDL1NaNxoixsbGLMsql8uSJDUajUOHDvU7R8SaYVlWs9mMx+PtdvvAgQPUMV0wTfP48eOXLl1yD3b//n0ASKVSADA+Po57ggQxmAy6TrNv3z6ceJ588kle7WDWM/V6/ZdffimVSt1iME3zp59+KpVKNqvhWCx2+/bta9euGYYhSdIbb7zB+mo2mz1w4MAnn3xiWdbXX3+tqqokSTg43rp1a35+vtFo/PDDD4VC4fjx4/l8vlqtYocnhoiJiYnvv/9eFMVGo0FLNYPGH//4x263lrX8xR1qRVHa7faVK1fWOmv+4b333jt58qT7uouu65IkZTKZU6dOoR/4/v37aQGMGFgGXafBlU8cnt54441IJGJ7SxgbG5uamnKPYWJi4vDhw/zFbDaradqJEydCoVAoFHrttddg6XVE1/Xp6enZ2dmxsTGMf3Z2tt1uo5Xc2NgYGiCLoohhJicnJUlyUaqIQebkyZMA8Ntvv/U7I8TvwIn2+vXr/MXvvvsOAJ5++mkvMeAONXZqwomqqoIguOw6IalUaufOnVgdY2Nj8/PzgiC89dZbG5JHguiZQddpACAUCs3OztZqNVmWNU3bv39/NBpd5Yv16dOnd+7cyXbrJyYmLMtCY/6zZ88CwNatW1ngRCIhCEK1WuXXsXkH4I67/sRQgGanjz32WL8zQtjB/SO+092+fRsAZFn28jgaCI+MjKxP7oYbVVWvXr3KVrtdKJVK/Eb/6Oiooih0UgYxsAyBToOMjY3Nzc3hUaGNRuPZZ5+1nZrQEy59Eq2Scapj7Ny5E5bsFgk/8d1338XjcXKQGUBwQZTfPLp8+bIsy2yvRNd1l3cbtATfs2fPeudz6ECFZnZ2ll0xTZOtf9ukKori5cuX+cc3bdokiuLGZJUgemXQdRqb6e7ExMS1a9ckSWq32xcvXly/dG/durV+kRMbAHr83rx5k7+YTqfxS0CoEBcKhQsXLnz++eceHyc2krGxsVQq9e6777ZaLTxmc3FxEc93RiRJeuqpp3ACrlQq/NeL6vX6wYMHL126RGuoNlRVTSaTTzzxRJZj165d+NoGv5cqAHz66ad4Pg12mUql8sEHH+COLUEMIn08w9hL6plMxvmFl3K5DL8/NB1+fw6681R121H3+J5hGAYfbbFYtCwLPwPEn6BvWRYud3eLnL9LrB8ehYwV1LGR4zofXkTLR1sbcH+cWCu8SzWTyeDHm+LxuO3bJpIksQ+eaJrGDrMRRRH3R9Y+34PNslLFkdOJJEksDC9V9hSTrSRJ5XJ5vQpADC2DM04O+pl7APDPf/7TZhf84MEDWN1OeTwen5mZOXLkCIu5Xq+jOeGrr76ay+X+9a9/8WdlLiwssE8eEgMOump3vDUxMTExMbHix4mNZ2pqqpsTwPfff8/+D4fD/E+iI2g46B7GKUYvvYYgBoRB33sCgFKpFIvFmPcgrp0qisIs9vHUmYWFBWZhg/4R/Hmj3377LXBbCUePHhVFEWPOZrPJZPLtt9/GL8vgiremabjciovegiCcOHGCjxzNFQHANM2FhQUAIH9ggiAIgugnfVwj8pI67gGVy2X8fiwA2D64ze+vY4Q2twjr9+8l7FnDMDBOQRAURbHtQeCXvZ13bZHb9ik6fuGZWCv621yJNYSqcj0gqRL9YnDaXsDq3zJ7INDP1ImhgxqMb6CqXA9IqkS/GJy2NwR7TwRBEARBEMtCOg1BEARBEH6AdBqCIAiCIPwA6TQEQRAEQfgB0mkIgiAIgvADpNMQBEEQBOEHSKchCIIgCMIP9Pl8mn4lTRAEQRDEWjEg59P0+XtPAyIFYigYnGOdiFVCVbkekFSJfjE4KxS090QQBEEQhB8gnYYgCIIgCD9AOg1BEARBEH6AdBqCIAiCIPwA6TQEQRAEQfgB0mkIf6KqaiQSqdfrzlumaWaz2WAw2PHBer0ejUYDgUAkEqlUKuucTWIZCoVCJBIJBAKxWKzVarkHrlQqGDgYDGazWfeQgUCgY/N4SHDpIHyYRCIRCAQ8erWQVIn+Y/WP/qZODB0eG0yz2czn84IgAECtVrPdLZfLmUymW+Mvl8sAkM/nLcsqFosAUCwWV59zwobHqkylUoIgYCUqiiIIQrPZ7Ba4XC6LopjJZPApAMhkMh1DGobRrXkMNWvSQRBN0yRJEgQhk8l4lJJfpUp4YXBmc9JphoBaraYoComrJwmg4tJteJVl2RkbDsqyLLMrOI8ahrGC3BIueKnKWq1m00tEUeRrx0YqlWL/N5tNAOgWWJbleDzuv9l3rTpIs9kUBEGSJE3TvEfoV6kSXhic6Wlo9p7q9XoymcSFZVyIVlXVNM1kMtnvrK0vrVbrzp07uVyu3xnxP1euXGm32wcPHmRXnn/++Xa7ffHixf5l6uHl/PnzALBv3z52JR6PV6vVbjtQR48eZf+Pjo4CwKOPPuoMVigUdu/e/fTTT69xdv2CaZovv/xyMBicm5sLh8MenyKpEgPCcOg06XR6fHx8cXHx0qVLqItlMpmvvvpq8+bNuq73O3fry+joaCKRwHUFYl356quvAGDLli3syp/+9CcA+Pe//923PD3EqKoKAPy0+uc//xkAqtVqx/ChUIj932q1BEGYmZmxhWm1WmfOnJmamlr77PqFjz/+WNO0c+fO8fJ0h6RKDA5DoNMkk8mZmZlMJqOqKr5+AcDo6KiqqrgjQxBrQqPRAICtW7eyKzihXr9+vW95eljRdb3dbkuSxF9EdfOHH35weRANwJ999tmvv/7aucwwPT1dKpXWPLe+wTTNmZkZURS/++47ZimPyqULJFVicBh0naZer+dyOVEUO74EnDhxwjTNjc8V4Us0TYPfv+4j7Xa7H9l5qLl79y50qgsAuHfvnsuDmzdvnp6ebrfbL7zwgs1tLZ1OHzx40Pt+ykPIlStXAEAQhO3bt3///feapgmCsH//fhe1hqRKDBSDrtOcPHkSAI4dO9bxbigU2rt3L/uJ5jXBYDAQCESjUb4fViqVZDIZi8UwjM3bU9d1dBmt1+vMHdTpO5rNZvFWJBLhn8Xr9Xo9nU4HAoF0Ot0xt7qu89mzeTxWKhV8MQoGg8lkstueWr1eDyzBcsVsjFhUiUQCC5tOp4PBYDAYRGm0Wi32+sVKh7ZK6NuMTs7BYLBQKHTMAEEMMpZlNZvNeDzebrcPHDjA+lG9Xtc0LZFI9Dd7A84vv/wCAK+88srExAQAhMNhXIDpZrZIUiUGjYHWaUzTxL3zbdu2dQtz6tQpFvjJJ58EgJ9//tkwjGg0un//flQvcPJGM9u//e1vgiCkUql2uz09PY0z908//TQ/P69p2jfffPPpp58ePnxYkqRqtfryyy+zdaBkMnn79u1r164ZhrF3797p6WlUa3766acLFy5omnby5Ml2uy0Iwo0bN5z51HVdkqTR0dHFxUVN09rt9vj4OBtws9nsgQMHPvnkE8uyvv76a1VVJUnqqNaMjY0ZhiGKIrsyNTWFHshIq9X69ddfS6WSaZrvvffeX/7yly+//DIYDO7fv79SqRQKhX/84x/5fF7TtEOHDmHGHjx4kMvl2u12Op0eGRn5+uuvRVF84403lj0OxGegJ6r368T68cc//rHbrY6WvzxsY7rdbuPCg2mab7/99ueff77GufQp27dvZ/+Hw2FJktrttnM0IKkSg0gffa6WTR2dOQHAi0uhoiiiKPJXcOJnjoUAwJ9vgXqAIAj4Ez0bFUVhj+NePh5VUqvVbJHz0sNnMaSmaR1df2VZ5j1LU6kUAGBmcMuDPwcFT0bhw9t8j52uyLbwACBJki1C3tm1Y4Qs5yicbsd79IuemusKfLnxIn8CCrZAF/9hYmV4qUq+eyJYpx6bJXYrDMxOJBq0MXBtWX0HwYu2M5mwXzi70kMiVcILg1PjA71Ow1h2s9Y0zVwuZ7MoxB0r9AhFdu7cyayMJyYmnO8fr776Kvv/H//4BwDMz88DwDfffKNpWoADw/D7R7iYFA6HnUYAuq5Xq9Xdu3ezK6dOnbIsCzNz9uxZ+L1paiKREAShWq2uxquLzwYaV27atMnjI4888siK0x1eXnrpJQC4desWu3Lnzh12ndhgcP+I7wK3b98GAI8+gDhojIyMAMAzzzyT+T0YiaIo7hPzwwau0Fy9etV5a2xszHaFpEoMIH/odwbceOyxx/Cfer3u7FE8OA/xOzKwpGS4qAV79+5tNBq//fZbx7u7du2CJYPEGzduyLI8NzfXWwGWQIPHbuBeFe9CDAA7d+6sVqt3794l47sNY9++fe++++5XX33F7AOuXr0qCAJ/RAqxYbz55pulUunKlSuTk5N45fLly7Iss9cSXdd/++039tNGvV4XRXHPnj0AMDY25hxAqtXqq6++6j6wPGxMTEyIoqiq6okTJ9gbzsLCAu9hWq/Xt27dGgqFSKrEADLQ6zThcBjVFHxdXpaOhiwuuK9b2JZbFhYWeoq8V/jlAWL1oMfvzZs3nbdM08TatJkIhEKhL7/8slQqoT11oVDI5XKzs7PeD+og1pCxsbFUKvXuu++2Wi007V9cXOQXACRJeuqpp7AS8UtDzLi+Xq8fPHjw0qVLVHfd6NZBLl26BAB/+9vfTNNEsQuCcOLECbxbKBTGx8ePHDmywbklCI8MtE4DAIcPHwaAc+fOdQugqqqu67ii0/EcEX7HxwYuZfObPjw4OO7YsQP/aprm9FTyuDeE2btw4YIz87C0SN5x9qXXnRWArmHor/HGG2/YPr+XzWY3b96MxhZPPfUUcxZDJiYmyuXy8ePHA4HAmTNnarUa+XT0kVOnTr3zzjvPPvvs5s2bFxcXG40GvyojiqIgCGhN/Kc//UmSJDz3IRKJnD9//vLly92WcB5y3DvI6Ojo/Py8aZqbN29Gr4u5uTmmGj7++OPgWBEniAGij7Y8HlNHK5mOhoHNZpNdx61cp6Utsy+G35vNWpYliiIzCsb3v3K53PFxtBVln9OzLEvTNGY66m6OypcC7YjZU2iOipE7DZx5g2WbTSumyIrm/LqN7afz0znuRsfO8INAf5srsYZQVa4HJFWiXwxO2xsCncYwDFQIZFlmOoemaZlMhp/18XgopnbUajVBEHgVB3W4TCZjGIZhGPh5QqYWoJYgSRL/OO8oxHaUJUniHQEMw8Avt7lrAKh2wJIBnSzLfObRDUpRFJY3SZKYFxL74C1zyUF9Kx6P12q1TCbDfLiwdJiWKIoshnw+D5xXFxMpypPFz6SB4ePxuJcK2jAGp9sQq4Sqcj0gqRL9YnDa3hDoNEixWGT+DoIg4HRuC6NpGqoXqHnwiy7W0joNCxCPx3kXcebLjcuqoijyayosDN5lqo+1pCoh7k6/zWYTNQlRFJ0KUD6fx8gFQUDlBq8zh3amk+F1VINEUUS9DRUaVPX48LVazeYnYovQdpc5LzC81M7GMFCZIVYDVeV6QFIl+sXgtL2A9ftZeSMJBDY09UAg4OK7lM1mp6ena7UambAMLBvcYIj1g6pyPSCpEv1icNreoNsIEwRBEARBeOFh0WnQ4XNhYaHbNy9dXH8JgiAIghh8Hoq9J9xXYj+dG0y8N+NqztYj1pXBWd4kVglV5XpAUiX6xeC0vYdCpyH8ATUY30BVuR6QVIl+MTht72HZeyIIgiAIwt+QTkMQBEEQhB8gnYYgCIIgCD9AOg1BEARBEH6gzzbC/UqaIAiCIIi1YkBshP/Q3+QHRArEUDA4pvXEKqGqXA9IqkS/GJwVCtp7IgiCIAjCD5BOQxAEQRCEHyCdhiAIgiAIP0A6DUEQBEEQfoB0GoLojGma6XQ6GAwGAoFoNFqpVFwC67qOgev1Ol6p1+vJZHJwTOcIgiB8D+k0BNGZWCw2MjKyuLhYq9Xa7fYXX3zRLaRpmtevXy+VSu12G6+0Wq07d+7kcrmNyqxvKRQKkUgkEAjEYrFWq+UeuFKpYOBgMJjNZm13eSU1GAym02nTNNct44OOqqqRSISp4DyVSiUajXYTo5NsNotij0Qi7qo/Qaw7Vv/ob+rE0LGRDaZcLgOApmneH8lkMgBQq9XYFVmWqZF3xKNYUqmUIAgoUkVRBEFoNpvdApfLZVEUM5kMPgUAmUyGDyDLsiRJWKeapkmSJMvy6soxWHiUarPZzOfzKCK+uSLFYpHJvFwuC4KgKIpLbIqiMKliFygWiystATGsDM5ARzoNMTRsZIPB0XkFj5BO4wUvYqnVaja9RBRFFy0klUqx/5vNJgDwgfEKXzuotrooSUNHT43N2Vwty9I0zaaUuKspxWLRpvpjm+/pZYDwAYMz0A3u3lO9Xg8sEY1GnavEgd/Tl0wydF1PJpP9zQNB+Inz588DwL59+9iVeDxerVa77UAdPXqU/T86OgoAjz76KLvy22+/AcCDBw/YlUceeQQA/vjHP65xvoeZixcvAsCWLVvYFZT/Rx991DH8uXPnACAcDrMrBw8eBICzZ8+uYy4JojuDq9OMjY0ZhpHP5wGg0WgcOXLEFsBaetPCV40+ZJHjww8/zOVyuq73NxuEaZrJZJLZTCSTSV4bZuYUsVgsGo12jCGbzQYCgenpaVjSm5lJQavVSiQSeDGRSHS0RfCevWg0qqoqXuc1+Gw2y/8MBAKYEGaM5QftITCeWCy2gswMOCgcfr7885//DADVarVj+FAoxP5vtVqCIMzMzLArW7duFQThwIEDTCX67LPPFEXh4yd++OEH25VwOCwIQqPR6Bj++vXrtitbt24FgBs3bqxH9ghiefq4RuQx9VQqhVnl15Z7jWRdMQwDN6c75pBYK7zUdTweF0WR393P5/N4K5/PS5JkGIZhGNioXOJx7j3hVgjGhtYYAFAul22PuOw9YTtRFAXzoCgK32ZQfZckCX9qmiaKIvx+cySVSqFxQ7PZZMYluP7vNIwYZJatStwEYdJAsAri8bjLg4ZhZDIZZhHCg4ISBKFYLCqK4r/e2tNg2HHvKR6P21q15bqFiuOeYRi2bPjMUIlYlkGYiJEh0GkymQwO99BpW3cQRJnJZHAsEATB1r2JNcRLXcuyzM95/BQoyzI/jdnmSxtOnUYURd5YEiddvsaX1WkURRFF0RYn/4gkSYIgsLs4B/NtXpZlTC6TyfD5T6VSPtNpUH2xTY0dLzpjRgRBsM3N1pIBrF8n3dXrNDjS2oyCXd5+cdzjm6iXOiL8xyBMxMjg7j3xbNu2Dcf3ZDLp7s/JvApxd4AFxsNCgsEghgkGg8FgsFAo8M922xdYlg8++GBmZkaW5Xa73W0jWdd1tm0xOGZA/mNubg4rTlVV3F26d+8e3tqxY0cul2PV+sorr3iPtlKpaJqGVhpIOByOx+PtdvvKlSteYjBNM5fL4eoO49ixY7BkOAIAhw4darfbzBsWDT7QZAEAWq1WOBzGHZbt27c3Go1sNos7a88995z3svgby7KazSZWzYEDB2zbwffv39+7d68kSdVqtaOV3kPOvn37RFHM5XI4Nuq6jhudqHw7effddwEgmUzi1mer1frss8/g9zuGBLGRDIdOAwCJRCKVSrXb7ZdffrnbSFQoFKanp8+dO2dZVq1WK5VK//znPwFA1/UHDx7kcrl2u51Op0dGRr7++mtRFN944w2m9Jim+eSTTwLAzz//bBhGNBrdv39/Op1eNmOqqu7cuTMcDqNx3OnTp51hTNPEyQw3HfB/3MVYmTQIF/CQkqtXr545c4a/fvTo0b179+7fvz8SiaiqOjU15T3OH3/8EQAef/xx/uLTTz8NAL/88ouXGG7dugWOuWHbtm0AwOZdtMdkB+F88cUXmUymWq1igEKhMDk5ibcmJiYymcz09PSTTz6ZzWa3bt06NjbmvTiDj4vpLm/525HR0VFVVRVFsWmc6XR6fn5eVdW5uTlFURqNRiwWW7Mc+4JQKHT58uV4PP7GG28Eg8EPP/wQr+N6jJPR0dFarSaK4vj4eCQSYaZOzz///AblmCBs9HGNyGPqmUyGLZBi1+IXNvlIcB+d/ZRl2fYTuK1ftC9mnqLL7gt0QxRFtvSKy9rODTJc0WVROR1NCS94aTB4NgmzQXHKuVarYUtA25pu8dj2nvCn7bwT20X3vSePmyloZKNpWrPZzGQyuMOFJjjOBqNpGoZ3P7hlAPFSlVgu/krHWugGio4Fdvpyo+j8dJhKT+N5x70nJz35ZqPFmG0gJR4G+qtL8AzNOg3y+eef47pxR8fpqampxcVFAKjX64lEolqtsnNdGcw5Ahf2ES/7Ah3BjYxEIoE/33nnHejk93j//n3+J7+FQawhuq7PzMwoiuIi4bGxsbm5uWKx2Gg0Pv74Y48xj4yMQCevEAB45plnvMTw2GOPQSc/EQDYvXs3+//VV18FgIsXLxYKhddffx13uFRVvXjxIi4E8oTD4dnZWZytDx065LEswwLuH/GbR7dv3wYA9IgnzAAAIABJREFUnGWXBbc/sOJgyVsKvXKQEydOgOdltoeTQqFQrVbz+bzHvaQjR4602+1Lly6td8YIohtDptOEQqFSqSQIAm8YwdNqtWKx2MmTJ1977TWPYx942xfoyLlz5w4fPsx+4t5Bo9GwOdbiwHrnzh38iXtntOW85ty9e5f/aduj5PXgRCKBh592iwqnTxbDnj17BEEolUq2KVYURY+bPuFwGC2u+HaLTYI/gmVsbEwURdzBRP37xRdfbLfb77777p49e1iwbDbLcjI6OqooiktZhpQ333wTAPjNo8uXL8uyzBRWXdddrOvq9booikxo2AevXbvGAqB4mdJD2FBV9Y033lAUhe14IvV6vePufzKZLJVKxWKR3tmIftLHNSKPqfN7Twi+mAIA/sOu43YSW0y2eZ3YfvKnlK7MyQIDdMTpbirLMvMxxlPe6ajNXlm2wRiGAUvOusViEXcqJUnK5/PNZhNdolDsWHdOvxgWDyq4zA/cWmpd7Bh4PF2e3/HBBsYeYR7+LIymaYIgMDfjWq2GWbWljjuVfPNwnk+Pfk8YD3p9D5dnsse+z3YS0fXdJnBevFg7qNtZloVGHrb9OHQrY0LDQ/395KjY03iOvYNv4YhhGOVy2daYGdg4+fFN07RisSiKYkf/eeIhob+6BM9Q6jQWd9QEH4koiryDq3edhvnl8kk4j2a3EY/HnboLjq3g2IFuNps4pKKeNFzWDwOClwaDzrqCIOAcjzJHvSEej7PtRVEUuyk0aGfAw5pfrVZjMcTjcb4S+fCyLNv0XdaKNE1j5paSJHXMg9N0RlEUW4PJZDJsGVIQBI8mJoOD9xEQjeRQ4LY+hZXLf7+JVS5TbniYYoRCQyulNSnOgOBRqs6XMXYLG383AVpL4xtToJlpWiaT8ZkwiZ4gncayetFpOtrxsbP4+Ah5nQbHOPbTRadhd/mEnJ8y4cFDzzrexahsZ5nQ0TWrZ3C6DbFKqCrXA5Iq0S8Gp+39AQYb0zS//fbbRx99lNnhMk6dOqVpWqlUYlckScJDO7Zv3/7FF1+ggXClUnnw4MGePXvQPFPXdTRkuXnzJnBWn7Ozs5IkJZPJLVu2jI2N4Xk2xWKxo9WLruuHDh0SRXHTpk3Ouzt27KhWq7lcbnR0FLeiL1682G63Y7EYbuGHw+EnnnhiZGTEWSiCIAiCIFZIH/WpZVO37QI4d6DwrBf2s9lsohlEPB5n59/jEat8PPy6PS8EL/sCLOfdcmWLGTcR0D7D5lcF5M7dI/1trsQaQlW5HpBUiX4xOG0vYPXv2LdAoJ+pbySqqt6/f9/mPtBqtV5++eWFhYV+5WroeHgajO+hqlwPSKpEvxictjdkvtzDiK7ryWTyv//7v23Xt2zZsnfv3r5kiSAIgiD8x6Db0/iA3377DT/pcPjwYXY+282bN+fn5z///PP+5o0gCIIgfAPtPW0E9Xr9s88+u3z5MpotS5J06NChffv2sUONCS88PA3G91BVrgckVaJfDE7bI52GGBqowfgGqsr1gKRK9IvBaXtkT0MQBEEQhB8gnYYgCIIgCD9AOg1BEARBEH6gz/Y0/UqaIAiCIIi1YkDsaQbFrocgCIIgCGI10N4TQRAEQRB+gHQagiAIgiD8AOk0BEEQBEH4AdJpCIIgCILwA6TTEARBEAThB0inIQiCIAjCD5BOQxAEQRCEHyCdhiAIgiAIP0A6DUEQBEEQfoB0GoIgCIIg/ADpNARBEARB+AHSaQiCIAiC8AOk0xAEQRAE4QdIpyEIgiAIwg+QTkMQBEEQhB8gnYYgCIIgCD9AOg1BEARBEH6AdBqCIAiCIPwA6TQEQRAEQfgB0mkIgiAIgvADpNMQBEEQBOEHSKchCIIgCMIPkE5DEARBEIQfIJ2GIAiCIAg/QDoNQRAEQRB+gHQagiAIgiD8AOk0BEEQBEH4AdJpCIIgCILwA6TTEARBEAThB0inIQiCIAjCD5BOQxAEQRCEHyCdhiAIgiAIP0A6DUEQBEEQfoB0GoIgCIIg/ADpNARBEARB+AHSaQiCIAiC8AOk0xAEQRAE4QdIpyEIgiAIwg+QTrNBqKoajUaz2Wy/M0IsT0+VZZpmoVCIRCL9qlzTNNPpdDAYDAQC0Wi0Uqn0JRvrQaVSCQQCrES6rmNJ6/V6fzO2Hui6HgwG0+m07XrH+q3X69FoNBAIBIPBZDJpmmY/skwQAwfpNF6JxWIBV2KxWLdnK5XK1atXG41GTym2Wi2WqPdhK5vN2jLGz7W2UvSUn7UlFotFIhHv4VF1YOO4izRUVfVSKS6Pf/XVV94r68qVK/Pz85qm9ZrQWhGLxUZGRhYXF2u1Wrvd/uKLL/B6vV5ncohGo06J2drJhmccWq1WIpHA1BOJhKqquq53Uw1N07x+/XqpVGq32xucz5XhMlAkk0nvapmzfiuVysGDB+fm5gzDUBQll8vduXNnXcviEb7JdcOX+igxQFiEN2RZLpfL7KdNevl8XpZll8drtRoAZDIZj8lpmiaKYiqVymQyoigCgHv8POVyWRAEABBFUdM0291UKoU5MQzDY4TrAeaw1zygGN0lieISBMFZ9p5S8V5ZvYZfQ8rlMgB0K6lhGPl8HiUWj8e7PV6r1dY5mx1AoSmKgm2gXC5LkrSsGDOZTL8y3BFFUVzuNptN20ChaVo+n8fGL8vysu2/Y/1KkuSe7nrTLfVarRaPx1lusbJYhWqaJknS4NTdyuiv5IlloXUarxw8eHBiYqLb3cnJyZdeemkNk7t48eK1a9dOnTo1NTV17do1URSr1arHZycmJr788ksAWFxcdN7dtGlTKpWampoKhUJrmOFe2blzJwCsIA+osnzwwQcd76qqyuIPh8OryOBw8OOPPwJAt5KGQqHJyUnUYkulknNfA5v02NjYOmezA2+//bYkSbOzs9gGJiYm5ubmUK0ZFnRdz+VyLgFGR0dtV8Lh8OTk5M8//yxJUrVa/dvf/uaeRMf6bTQaTzzxxEpyvBa4l3pmZqZbawyHw2fOnFm3fG0EuJTY71wQbpBO45VEIuEeYHJycg2Te/3119l8HwqFIpEIvtt5ZGJiIpVKtdvtZDLJX2+1WhcuXDh16tQaZnVl7NixQ5blFTwYiUTi8Xi73WbqC8+5c+cOHz686tz5ik2bNuFqzczMTEeh9QXn7l4oFPqf//mfvmRmBZimGY/HV/ZsKBQqlUoAUK1WB6dGvOBe6rGxMfcXidHR0b4o0GtCq9WyDafEAEI6zVpimmYymURrvm62e61WC41CotFoq9XqFhW/gGGa5sLCAi69eOfUqVP4LlgoFNjFQ4cO2V6VstlsJBIJBAJo5YoZ5vfFWTCbhYqqqolEIhaLYakxBttmObNktNkTAMDIyMiOHTtYAdGuIhgMJhKJZdXHN998EwCOHz9uu46pP/PMM85H+KqJRqPOiaRSqTBjnfPnz7PrNjsAp2RsOAXFbJiYpUhP5e1YQSyh6elplkkXI+Vt27YVi0UASCaTLq2OTw5tXFjger2OAsQwwWAwGAzyTQs8CJknHo83Gg3bJLFnzx4+NrSg6lYu3nSMSZtdZE/xNcu6pGmazBJcVdVgMBiNRr0LRNf1Xbt2oVrm0hhcCIfDiqIAwLlz5/AK61B8QWz1y9Kanp7m07VJnllV4zSM9mfYDtktW7tyypzZ88ViMVycWH2pGR1TR2sqHEbY0IEjDAAwQ2m23IiVGIvF+NxGIhGbmXxPDaDbGF6pVJ599tl2u12tVjFXy44MvQofeh8JiQ70e/NrWOkovXg8zkxYcC85n8/jLbQeiMfj8Xg8k8ngEoUgCM1m0z2hYrEoiuLKbDWazSau7mAqqVSK5QeRZVmSJMwwvspLkoS3DMPAXR4WGLf20ayn2WxiAXFrv1wuoxGPIAgsPG9lYssJ3mWZicfjuEutaZosyy6WQ7VaDe+iAHkLJ4ynXC5junwkhmEIgoCmG2hWCQCpVIoFwPke81Or1TCrTOb4YsrsADRNwwAdS2otWVHwGWA2TL2W16WCEKyFbo+zMJh5zIYoirwZB/zeLIyVlLVYzCfWPsqtWCzWajXcJ2IVuqyQbbAmIYpiRxuLcrmMkucbv82ehjVC/sFUKsWMHorFok2AKO1arYY5lGUZu21HMXYTCIKNsFsBEZdhlokUI8ey2BpDx/q1ycQwDEmSsPWizQrmGWsNhYxNjj2oKIqtpvA6GsSw8NhJV1BqPvPOsatb6symSlEUbLTYYhVFwbGLtTrs+ExoiqJIkpTJZNgaEmuWvTYAlzEcJc9XkMvIsALhW72MDEQ3SKdZIR2HKuwefBj20zkgYofpaLnJR8i0z5WpNWwiZNoAAydy3vzQ1sGcg5etS9umExyAWA/HDm/LScdS8NqJYRhedBrMPB8SraqtJVHztxRFwVsMHMIwqzgS8RnDyNkVp12qTTJOG2FbBmwBPJZ32QqyetRprKVKsVUiH5LXSmVZtv0Ezqwbp2SWGXchd6TZbLIWLsuyM6RTsM66EEVREAReS2O2t6hm8QLE5Jw6imEYHe2svQikW+kQF52GGbzzgVeg02QyGd5w1db+MZM4x+PfWq1mqyk+G/g4r4yiGtFTqfnM27q8e+r4CP+ugq2I1a+tSeBPSZJYAByFWLX22gBcxnDLUUHLjgy9Ct/7SEh0g/ae1pK5uTlcb8dVTQC4d+8eH+Dpp59m/09NTQmCcPnyZfcINU3DnjM9Pb2Co0cmJydxkf+FF16YnZ3lb3300UeCIPD732gSdPr0ae/x83tkmzZt4m/Zyr5t27ZukUiS9P777+MSbigU2r1797LpJhIJtJtmu10ffvjhyZMnnSFN08zlcjbj02PHjgEA7jFduXKl3W7zO1ZbtmxZNgOrwWN516SCbHz++ee4I9nRMmBqagrtyuv1eiKRqFarTsdpVuOPPPIIu7iskDsyOjo6NzeHK5HVanV8fDyRSPR61MrJkyfb7faVK1fwZ6vVCofDmMlr1661221RFNmmABraf/fdd+xx7JKhUKijIYgXgfSdCxcu5HI5Vsbx8XEAsLkUoLUy/v3mm280TeO3gzEMv3HM9+W1dSbwkjrftPDEB/c8vPLKKyzA0aNHAQDH1RU0gGXH8BXgXfgrGAkJG6TTrDGVSiUSiVy9etWLhf/OnTuXHSLD4fDU1BS+srOjR3oCrU+cfkCNRgPfgRjY69bqqBVMjrkJPHjwAABGRkacIVFW4+PjsVisXq9PTU15iR81mM8++wyWdsc7bj/funULlrylGKhgYd7+/e9/w8b6/ngs73pUEFqnCoKQy+U62rugXcLJkydfe+0170bcywrZhUQisbCwgCsipVJpWVcgG3v27BEEgRlXFQoFZq2PTkPONzmPDQxZmUC8gD1i9TQajW7Lnx25ceNGxwWAjekC6516KBSSJAnH1ZU1gJ7G8F5xL/7KRkKCh3SatSSdTh84cODSpUuzs7NON87VgMsSq39jsNHrMYA98fe//x2P2DFN0zTN999/X5KkjmrH6Ojo999/XywWFxYWxsfHPToX4GRWKpV0XT979uw777zjEvjGjRvusW2ki6b38q5HBYXD4fn5eQDYv3+/zV64Uqk89dRTeJ6by8kF3VhWyDw2++Kpqan5+XlBEKrVqrsVs41QKKQoiqZplUrFNE1d121dbzU1u0qBuPN///d/ALBi5yme27dv9xR+YWFh9YmumPVO3bao01MDWL8xnOFS/JWNhAQP6TRrhq7rMzMziqJ47wkLCwveR7RIJLK2B67gW7Vz/lirl9FwOHzs2LF79+5t3rx58+bN0Wh0bm7OJTy+r+O5qF522UKhEOoxqVTq9OnTr7/+esdgjz32GABcv37deQuXdh999FEA+OmnnzyUaS1ZtrzrV0Gjo6O48vfss8/y1996661ueqc7ywrZCepVtlyhwdBvv/3WU+pY9Z9++unZs2cPHjzIrm/fvh0ALl68yAfGJT2PMa9YIMvCTnnBZdTVIEmSqqq2PTubysizY8cOTdNsLoqVSmVj1PoNSH1hYQG3QXttACsYw3vFS/F7HQkJHtJp1oy7d+/yP5c1C6jX65qmvfbaayy8y6nheDA8fwSOrus9vc46wXNc+LEP+xWbFXA2Yp2t1+QqlcqZM2fm5uZwcZWdruaEfx05ceIEAPz6669eksDJrFQq7d27t1vk4XBYlmXbeTZ4lvy+ffsA4MUXXwSA999/v1uVoakNO34eXevdMybLMh/m5s2b/F2P5V22gmDpBX3ZxuY8Oz+RSOAJRvxF266Wd9OWZYXs5N69e855F/ODGpJ30C+6Wq1euHCB1z927dolCML09DRLyDTNI0eO4HmPXlixQNxhp7woiuK+5+KsX2wD9+/fZ1deeeWVdrvNPK4BoF6vu/TW5557DgBeeOEFNuDouv7pp59uzBmV65E6Lw1d1zVNw4OOem0AvY7hKxgZ3Iu/4pGQ+H+4mxATHWHnzfOe2IZhAIAgCMVisVgs4piFPpbNZhP9e0VRZF6I6PjKHsfwzCFTEATmCYL+mcVikc+DzTXaBXQE6PitAHyb4b1A+Szhq3w8HkefSfRzQRchwzCcHgd8Eawlm395CfzOQ0cvGOC+1YB2Fd0O+8cvRThdgfgraFLNR4LyFASB+TtgNdnkIEkSOqVjzpnMcWLDu8Vikbnip1IplL/ThY05KKE/KvM+Q+F4L697BTF/e5uLPg96T3Rzr7P5prGvE6AfNUaOpUYXEl7UNi/fZYVsA2WoKArK0DAMFCP/iFOw+JSzvN0+T4FtGLseei3Z3Nni8bjLBwpcBGJxBwqkUqmONej+bQSbozsWgfe071i/KHZbMGadjc7/zBEMnQHB4X2G7RPbJO8KxMTCmhnLAxtqli217UFn23NJ3TaGsEhYQszhEQuIQmMtDfsI74zZUwNwH8Mty4KloweYx7XLyLAC4XsfGYhukE7TMy56YbFYxGEdRyscXNgYzc5+YN2AjxY1D3aRhRQEAbUKWzYwcvcWz5xFGTbzNMMwUqkUOybEOSWwE02wFDgiMFcshi0hdoaNIAg2u1HoNPGIosiCybLcUVHrmIRlWZqmsfHXpbyaprkInx0UAQB43A5Kgw12tpqVZZlNxradIBYhU4yazSY6cKJm4LG8y1aQrQqgk9e0s5qc8fMTQLPZZPMQJg0AqVTKJlg2dttK7S5kG/l83jAMPD6k4yN8EliPHWuWwavXPOzUE1EUbQq3Lf9OugmE3cVW0VF1gy5IkuTUBmw15bwCjl7GCwEbMDsNBSN31potRSwa/w0mm1g6xuBe6o7F8Zi6rWheWh3zx8Yqxh5qawY9NQD3MRw1JFEU+fNvOo4MKxC+1cvIQHQjYHXvewSxGv7/9s7vxY3jDuAj6GtzWalPjilFq0BNAxfsPbuEiyGBdsXVDzZ1WTmBYnC46+qCH+pU5+7ZhFLZ9V7TFAw+ScEGP0V7vRiHklXvzpADS4Q4Vo1EYxzwSZg09ElrJe4foD588XQ8K61Wpz1pd+/7eZJ2Z3fnOz+/M/Od76TT6bm5OW5lulQqXb582dmwBkEQxA2VSuXVV1/VdR23CCEA2tMgO0KpVDIMw25q98ILL6DTBQRBEGQn+N64I4CEk3//+99gt3js2DHqbe8f//gHIcQPJ2giCBICwPr+3r17444I4hdw7QnZKQzDuH79OvVnqijK0aNH8VQ2BEE8IZlMsu6SsS9DCOo0CIIgCIKEA7SnQRAEQRAkDKBOgyAIgiBIGECdBkEQBEGQMDDUvid6TjqCIAiCIMi28cS6d9i93GhijHhIJIJG627Z5WmF4qP4446Fx4RSKPd4NUWCa08IgiAIgoQB1GkQBEEQBAkDqNMgCIIgCBIGUKdBEARBECQMoE4TDOr1+tLS0vDvqVQqhUJh+PcgCIIgiN9AnSYAGIbxt7/9LZPJwN96vT41NRWJRBKJhF1BqVQq6XQ6kUhEIpFIJJJMJg3DsCwrnU4TQqanp3/605/C7/DRbDYjDIlEgrubSqUikUg0GvVEQQwKhUIBykMymazX6+OOzkipVCpQWSKRSDqdbjab9jDpdJotNoZhjD6eO02z2VxcXIRiwBb+3VApDMNIJBKVSoW7blnW4uJiNBqFtqJrvvu27vQSCnAu0r4Vyhs6Q+Dy8Uajoev6MB/yD6qqjviLtVpNkiT6t9FoiKJYLpfhtyRJxWKR3tU0jRCiKEqtVqOPy7JMCJFlmQbL5/OjF8QNQxZIVVVlBtM06a1GoyEIgqqqrVarVqvB76HjO05cppWmaYIgQIFRVVUQBFo2Ao0b8cvlMmS0ruuSJBFCBEFoNBpsGKhQtMwoirJjUfaSgWpKPp+HFsA0TVb84FYKl+LXarV8Pi8IAiEEqgCLLMuSJOm6DvWCEKJpGhtgxHXHE6E6/Yq0bxuEIRv//79nBJGANmWYD/mERqPhVbq7pNVqiaLIai35fD6fz7NRosqKqqqEkK5JDZ09e0UURfY9PmGY5G21WpyMLLIsC4LQarXgb7FY7NUiBAWXnTpXJKCx28l4jQg34rPKPfwlhHDdtq7rrO4bFNzXFGgWulb24FaKgRoKXdftcpXLZbYk1Go1GORTnW/0dWd4oeitXkXazw1CYHQaqCch0GlarRYM9Ub5UV3XBUFgr/TSaaCwiqLY9T32/h7eTJsznzBM8uq6zip/LKCMsk1Yq9WCCa1tf27suEkr6M/YoTnM5PlkZDYMfcVvtVpceYBiwFYEqNQ7Er8dxmVNgRmargpNoCvF8N2/PU2gstBgo687nug0zkXazw1CMHQaSHcK1WxM06RTwTDzSa8riiLLcqvVgikyQRCgYYIlGOi2aQaYpgkzEK1WC3JLEAROf6rVajA+4xZl6LdqtZooinRSWtd1URS58DCbx8kCP2gTCUs8VExoUmFus1gsCoJAi1qvKNkRBIHTRXqtPcHXHaZeuGlV0IF6KQHjYtvFutVqwWSsLMt2oaBl5woGZOg2I+oD3EQe0oS9EpoxxvbyjuuzoRaLoqiqKrcm5XPciA9LS71G4YGuFF5NadiD0dZ49HXHE6Gci7SfG4Rg6DSdbpNd0NNDctOF3s7TZUJCiCRJqqqapmmaJtQx0F1M06QBILxpmvC4LMuapoHKyXbtoK9AxsPiOkxOsN+Cx6F8wEUanmsBIRj9C9OVbJMBEQBhYW4TAiiKQhuLXlFyk3T0u1S9A0lhgOWm3lL8OSbbdrEul8tUp+QU387T0Qk3Hwvh/TBA2R590woG4tygzV6qA8o2igqUeVblVVWVHatwer+fcSM+NEeapimKAp2Zoii0qQl0pdgJnUbTNDrPPZa644lQDkXa5w1CUHUaGE+z+iPVJ+g72UQHLZLNGE6xIISwVk6g5dD1Gm7UDuWARgY6P6jk8AZurQfWm3t9Gt7A6jScsGxxabVaILVzlFgcbnHAh8izk4p9gUfchx8Bw8eHKjdsMePKmMPFANE3raBUcMP0rheDyDaKSrFY7Lo422q1oOIHSK1xIz70bbquswNISZKgxQt0pdgJnYa1XBxL3fFQqK5F2ucNgled0aj3ct+5c6fdbouiSLeZra+vE0I+++wzGiYWi9Hfe/fuJYRMTEw4vPPgwYOTk5Pwe2ZmRpKkdrtdr9cty1pfXz9x4gT91sLCAiHk008/pc8mEgn4HLwhk8k8fvyYEFKpVFKp1Pr6ervdHlLk/fv3g1DxeNxNlDheeukl99+Kx+PuA3OraeFgenp6bW1NVdV2u/3ee++NOzqIX7As69y5czdu3LDfisVimUxmc3NTEISLFy923e8dRGBcnslkoFmYm5tTVbVarX700UfjjprvKBQKkiSlUqlxR8Qbwlqk3TBqnebLL78k3dQx6nxleH7+858TQv773/8+ePCAdNNk19bWHB6v1+vJZDKbzf76179mlzM8YaAogaLz3HPP9X3t97//ffjRy11BVzj3LWFieXlZFMW7d+/C3+eff75XSJp04cNBNIcECSvnz5/PZrN08GNncnJyeXmZEPLVV1+NMF47CyxSU44cOUII2dzcJLu1UnSlXq/fvHnzypUr9Eo46g5XpMMhVF/G43NvR9VGblLnm2++cf9sqVR6+eWXT548uba2NjMz43XUBovS66+/7jLw5OQkTLoMJGwQqVQqkWfppcbNzs7SOTaYKrt//z4bACYIHTq5oAOiffHFF+xFmBCFBNk9GIYhCELfUTgEePLkyUgiNQq4aWYYIH377bdkt1YKO5ZlLSwsLC8vs+sDoak7bJEOjVDOjFqngZUUbvLTsiwPfXc+evSIELJv3759+/YRQq5fv84FcDgc4PTp0zs6A7mNKH399ddu3jw7O9v1zewnOFUS2q9gsWfPHv1Z9uzZ0yswzNgRQmC+jfWYCUlBd5+FFUVR2u02m+9QOzyfgPQzhmHcvn37woULLsMfPHhwR+MzMmArhn0ACYOlXVspWCzLevPNN3Vdt6/ah6nu0CIdJqF6MWqd5tChQ4IgLCws0F7csqz5+flh2hHLsti/GxsbqqrGYrFYLCbL8vr6ejqdpmGWlpYcrHNgBbrXm+3Isry1tUX/coMeOwNF6ZVXXnF+G0smk5EkaX19vauD83q9/t1339nrbeCKcjwezzxLLxOi1dXVd955B35PTk7KsszqzTBYefvtt0cQ5zECAt66dYte2djYkGV59wzEQaGBGXjAYQRlGIamaQMZpfmZM2fOkGcHkDCPe/z4cbKLKwWFKjRsdaAdUzjqDlekwyFUH4YxMHbzON37Y5ombOGBrUyEEPBgyHqUgd3RdC9S56mtPnUMRR3f0S2I8Cpd11utFnipYTe8gMNvQgj4aWB9JlIndexeIXg5+GGkG7BN02R9wJimqWkaPEVd95bLZU3T6M4C2GINpuns/knnKNkZyMkjTRxIbbgIB1PYXZ6HzD8NuP+hbntUVbX7W6MSz+H5AAARL0lEQVSu36nL/OEjPEZcphX4earVarR2+H+nrhvciA9+obiJPVrlqYMWqJ7FYpGrqn7GZe6zG7ah2LP1IriVYqCGAmaeON9d0FoqisKWDVVV2RQYcd0ZXig3Rdq3DcKQ2sj/3zOCSFA3LaxvPc7DSsfmoI/zOAJX2L+gCYEOwbqw4/YzUwd3giBomgZxsH+LBgY9BooCdfBA77JuADtP/fNCHGq1Wrlchg2B9HpX3bFrlLoC8XSTyJRisUg/LQiCoihd9/vBiSF+a8G3XayhohJH/2n06Ct/ngsxKO7Tiu7qtNeO4NJXfHDrYId1fUlNaLu6avQz7nOfVg1Jkuwu8wNaKVyKz3UZ7FOc9TSFS6JR1p3hhXJZpP3ZIGy78eeIdJ5OdWyDSGSoxz0hEonIsuy8lSm4WJZ16NChbDbruYnP1NTUW2+9NTc35+1rh8QPJSoo7PK0QvFR/HHHwmNCKZR7vBJ/PPueEJfEYrEbN2785S9/6WvZMxClUkkURb8pNAiCIAgyDMHWacBof2try9su31dMTk5evXr1/fff9+qF9Xr9k08+YZ0xIAiCIEgICLBOs7S09PLLLxNCGo3GD37wg4HczQWLycnJU6dOdd3QNCj1ev3zzz/nnDEgCIIgSAgY1p7Gw6ggCIIgCLI78cSe5nt+iASCALvcSm4gdnlaofgo/rhj4TGhFMo9Xk2RBHjtCUEQBEEQhII6DYIgCIIgYQB1GgRBEARBwgDqNAiCIAiChAHUafyOYRhTU1MuN3JbllUoFBKJhCcbvxEEQRAkQOysTpNMJiPPwnqRYa8nk8kdjYkDlmVFo9F0Ou3+kWazubS0FI1G+8Y8nU5TGbehZxiG8fHHH1erVZfhb926tbm5yZ0uHj4sy0qn0zT9wfWic/jFxUUIz56ITqlUKlNTU5FIJJFIlEqlHYv4GGg2m6lUCkpgIpGgxw73Iqxp1Ww2FxcXE4mEc02EIUEkEolGo0tLS12deUIASrPZ3MmIe8bi4qKbrSWGYbDScQ1jsHKfxhYEcZ9TlUqFtjCc5zOf5L5hGIlEYiCvbL2EClae9meYw6L6Pt5qteCkUGI7nrrz9ABI7qjY0QOHgdOT7dxDD8Lsekhkp9OhugV7fuegwIll9Ohyz8P7CjcFEg7UVVUVTmJXFKXv0bKSJEmS1Gg04FlJktjsgMMO4QA/ODQ+EMcZukwrOGwZ5IWzl53LRlDSaqC2C1ohWZZN03Q4tA9O7dY0TdM0OMvW3iwUi0VJkuSnjKuiDdp004MP+4ZkpZNlmU2uYOU+PWlc13U42VEQhL5HNsJp1YQQVVXL5TLXbu9o7rvM01qtBicQO3Q9HA5CBStPXb1nBJGA0627Kg3QygwTB0+A9m7Qp6AFBHWtawBVVSHAMEUfdRoOSFX6F7pt9goHqJ608oOiSdMHHmdzX1VVH55YbsdNWkFfzl6BU5p7hQ9QWrlvAaE173voNAyxqCytVgsqL9fEDzM+8ZCBOgCqnvZ9qlwua5rW6yXByn1FUdihjqIo0Kk7PAIJJQhCL11hR3N/oDzlqqoDDkIFLk/dMAp7mgsXLkiSVK1WuSnfQqFw4MCBmZmZEcTBGUmSXn/99W08ODs7KwjCysqKfQbSsqyNjQ2oSIiH5HK5RCJB/8ZisVQq1Wg0es2afvDBB6IoTk9Pw994PC5J0qVLl+DvrVu32u32yZMnafgjR4602+2PPvpopwQYId999x0hhF1AmZiYiEajvcKHL60KhUIul8vn831PbL1z5w57ZkgsFstms4SQr7/+moapVCrxeDxw54rMz8//9a9/dRPtbDZ76tSprreClfuWZR09enRycpJeuXjxIiHEealofn6+Wq1ubm7SKsAS3NzvJVSw8tQlI7IRXllZEQRhYWGBmj40m82rV6/+9re/pWFYI4mpqSnDMOD60tISZ3NDzXRASQLDWDCkrdfrcDeZTHLFl66Us8AbRFF86aWXIFi9XqeLi6lUqq8RzNmzZwkh7733Hnf92rVrs7OzExMT9kd6SUoplUoQh2g0+uGHH9LrnFlSpVKhV7rGjUso+xu2Ie946Wo6Ay3Xl19+2TV8o9FgdSBCyNTUVLvdhhT4+OOPCSF79+6ld3/84x8TQm7evOlpxMfDK6+8QghJJpOg1liW9cEHH0BXbSd8adVsNn//+9/LsuzmCPqZmZl4PM5eAUnZKpzNZnO5HDQ1QTk3t1AosHqqA5VKZX19XZKkVCplN9QIVu7DUIe9Apn7/PPP93qkVCqtrKzous5qQixBzH1noYKVpy4ZkU4Tj8eXl5cJIb/85S+hNCiKcvXqVarzWpb14osvEkIePnzYarWmpqZOnDixuLhICMlkMmDyQllbW4P1LODBgwebm5vVavXevXuFQuHcuXP5fH59fZ0Ns7S09Jvf/Ob69eudp6uGMAOfyWQIIfv373/hhRcg5GuvvXbmzJlOp3P9+nU3xrmnTp0SBCGXy3Gl/NKlS11HPA6SAoZh/OIXv3jrrbc6nc7f//53VuPpPJ1BBaanpxuNBiysdmVtbY3aMwEwwc5eGVReP8Al9U9+8pNeIR88eEAIOXDgAHvxRz/6ESHk/v37hBAQed++ffQutH1ffPGFhxEeF9PT06qqVqvVQ4cOVSqVN998M5vNcm09JXxpde3atXa7feDAgVQqBUOIVCrlvjd68uQJIeRnP/sZ/IUHBUGoVqsLCwsvvviifTTiN5rN5s2bNy9cuOAm8P379yVJarfbKysrr776KlWFgcDlPgfIcvTo0V4B3n33XULIxMQEDAWj0SjbLAcx90k/oYKep90ZZuFq0MehP9Y0Tdd1zuCDM5LodDqwmE2XAMmzJi+c1Qj8ZVeCucVjbtUQYmJfX4T30NVE0zQdDFOoFLBgz4YsFouwcAurnuwtZ0lBR+Fexb7BvowKOopzyrAvZN8wkLwjwE2JAh2OtfWzJ7LzLfZi11owfNUYAe5jSJV758wNVlq5+Si1ZoPSAvo9Z/XsgKqqXc0vGo0GVHlCyLjMAV2muSzL1KaEaygcKBaLdhPpwOU+BwjV6y6YjsGGFdh8QI1q7SF3KPcHEsqNPU1foYKep10ZqX+aK1euiKJ48eLF1dVVmCABLMvK5XKghVB+97vfEULYlZe+sLPE3Kpnu91m/+7fv7/rG0BjnZ+fh3Url7Y+77zzDiHk0qVLdFhz7tw5uMjRV1JY4IQlA4CdGPSc7ck7Xv70pz8RQhRFgTiXSqXV1VVCyA9/+MMxx8yXWJbVbrfBNHhhYWEgnwVBB9r0TCYDo8+5uTmYtXJjLlCv1zc2Nv74xz/ab8GsMww2Tp8+7XWsPWNpaenYsWO9VlIcSKVSd+7cASPIQMxG9MWyrHPnzt24caNXgP/85z+EkIMHD6ZSqVgsFovFlpeXRVHM5XLcendQcp8MIlSYGKlOE4vFZmdnCSG/+tWv2Osw6Q0jAwosKHi1+18Uxa2tLfoXbCf37Nljj6FpmhsbG6Iogj8DVvfqRTweV1WVmlaVSiVJkri1eaCvpLCQ6Wbx2xO2J+94mZuby+fz7XZbFMWpqaknT56AwkrXCFi62jOxt3qt3Dms6AWLZDI5OTl54cKFarUqSVIul2Mnn1lCmVbc+OHIkSOEkM3NTeenLMtaWFi4ceOGg0FoKpVSVbXRaPjTtKJSqdy7d8+NIVFXYrHYysoKIeRf//oXXAli7lPOnz+fzWb7qnfcwitM53/++ef2kD7PfRYHoQKdp73wkR/hf/7znzv38suXLz9+/BgMYOv1ei6X0zStq9oxMzPz8OFDXdcNwxBF0eUw5Y033iCE/PnPf4Zvvf322w6B+0o6Sj9O25N3vMzNzW1tbXU6nbt37+7duxdmg7t2P6Av3rt3j7346aef0lsHDx4kz5oeg3UkXA86hUKhWq1CxxaPx9fW1iRJunjxYtcCFsq04iZon3vuOULIt99+6/zU+fPnT58+3bcLhFoPAyS/kc1mV1ZW2P0Q6+vrhBD3Dk7j8bgsyzQBg5j7gGEYgiD0MiNj4UoLqPK98tfPuc/iIFRw89QBX+g0MF/S1S5pe1us7czMzKRSqdXV1Ugk8tprr509e9bBbi4Wi2UymYcPH0qSdOLECTea+PT0NPingrn9XhMtfSUFs/yvvvrKnVjesA15fYJlWSdPnhRFsesaASFkenoazPrYi1tbW4IgQB4dO3aMPJ0/A7755ht6PejcvHmTnaiIxWJ/+MMfyNNJaY7wpRU4D7QrcM6tSjqdPnz4sMt1WFEUuw6Nxs7Jkyf1Z6HWReze3b4cPnwYfgQu9wHDMG7fvt3XShpW4Tc2Nuy3WEsADt/mPtBXqIDmqTO+0GnogICdJIDEPX78OPyVZZldPIKNGO5ZXFwUBOHu3budTufx48e9VlgqlQqNA+0AICZ9gbXVXC7n0GT0lRTM8t99991eigWURRoly7LYZLEDvdGjR4/oFXYgPoy8Y8eyrGQy+fjxY26NoNlssiOPs2fPNhoN1olAo9GAHfiEkOPHjwuCAHsagdu3bwuCQAteoInH49VqlS1LMFFBV13DnVZnzpwhhLDWM1yrwolPnio07Ji+Uqn0Mj748MMPL1++7Hm0PSGVSmWeBXbpZzIZKp1dfJZms2lZFg0cuNwnTxUa2HILWJZFWzxW/FgsBmtJ7Cb2R48eOWyD92fuDyRUEPO0P6M0VKYbie3eGGG/D/V1CG6tWQ+edG8ReLqkWxjAPSgYgVNzbuoDlNr8E0Jg6xP1aU13Q7Cw3wW/+73OTIC73IEPoihyLm5h8ZKVt6+kMLCWJMk0TdM0IcUkSYIwYPYId4vFoq7rEEDTNBAWkoJ1bSyKInzCNE3w+w4BTNN0L+9ocFmiarWaruuCIMBAnLsLi8GsC1Hq47/RaPTy9w+JAOUqNGcjQGGjqVSr1eBYCRoguGnlsqhAuwH7U+x1jRNfVVVJkti5DU3TaI2AUzhoZYG7Hkvlmm003fZ9T6z44C9DURQoKuVymfPD2wla7heLRdhDyk1W0RaDy33wtyuKIlyB8wfo3RHk/kB5Cj2L3Tv2QEJ1gpanrt4zskjQ05Eo3K7RRqNBna9An83epfqQJEm1Wq1cLouiCFvUOIcr9GQT9iv5fB66di4O3F64crkMbqThLj0ox1kWKkixWKQFwkHevpLSvYKqqpqmKYqirus0JlBXBUGASiXLsqqqUEy5pIDwtVqNnuEAtZEeSeFS3pHhpkRBVGVZ7lX3QCJW16FJColmlxESGbLD5REqY8dl7avVarSwQUFi7wY3rdw3PrDnq2tdY8Vn3Vmx0K6L7nAWBEFRlPGWE/fiU+w6DSs+HYBBQrENDktQch+6ajvsmK1r4aeJwKl0I8h9l3nKdXAOeQo4CAUEJU9dEuk87SS2QSQy1OMjw7Ks+fn5K1eusCsUlmVdu3aNEOL/nT67h6CUKD+wy9MKxUfxxx0LjwmlUO7xSvzvDf8K//P+++8Tm8eaWCw2MTHh4IIWQRAEQZAAsSt0mkajsbKyEo1GDx8+DC7snjx58sknnxw+fHhknmAQBEEQBNlRdsva07Vr11ZXV2GfKvgqeOONN1Ch8RtBKVF+YJenFYqP4o87Fh4TSqHc45X4w+o0w8cAQRAEQZBdzvh1GgRBEARBEJ/gC597CIIgCIIgQ4I6DYIgCIIgYQB1GgRBEARBwgDqNAiCIAiChAHUaRAEQRAECQOo0yAIgiAIEgZQp0EQBEEQJAygToMgCIIgSBhAnQZBEARBkDCAOg2CIAiCIGEAdRoEQRAEQcIA6jQIgiAIgoQB1GkQBEEQBAkDqNMgCIIgCBIGUKdBEARBECQMoE6DIAiCIEgYQJ0GQRAEQZAwgDoNgiAIgiBh4H++kGFR6ZXHIwAAAABJRU5ErkJggg==)
2.3. Meshing
Because the size of the mesh division will have a greater impact on the calculation time and the final analysis result. In order to make the effect of the mesh division on the basis of satisfying the calculation accuracy and save the calculation time, there are differences in the meshing of different parts. This time, the mesh of the model is divided into 0.005 using the size controller for the solder joints and copper pillars, and 0.02 is used for the chip controller. All of them are mapped grids, which are divided into 1334400 grid cells Figure 3 shows the meshing situation.
2.4. Loading loads and boundary conditions
The thermal cycling load is determined according to various conditions that may be encountered during service. The temperature range is −50 ° C to 150 ° C, the temperature rise and fall rate is 25 ° C / min, and it is maintained for 10 minutes when it rises to the highest temperature and 10 minutes when it is lowered to the lowest temperature. The cycle period is 36min. According to existing research, the stress and strain of solder joints show periodic changes during thermal cycling. After loading for several cycles, the results will stabilize. This model calculates 5 cycles [7], as shown in Figure 4.
The base plate is mounted on a tooling fixture. The bottom surface of the lower chip can be imposed with zero displacement constraints in all directions, and the two symmetrical surfaces of the upper chip can be imposed with unidirectional zero displacement constraints.
2.5. Stress and strain analysis
The simulation lasted for 20400 seconds. After the simulation, check the stress and strain diagrams of the entire chip using the POST_26 post-processing program. It can be seen that there is basically no obvious stress and strain on the chip part, as shown in Figure 5.
Enlarge the stress-strain diagram at the solder joint. As shown in Figure 6, it can be seen that the outer part of the solder joint where contact with the upper and lower copper pillars generates a large stress, while the interior of the solder joint generates a large strain. The strain is gradually extended from the center of the solder joint to the periphery with the load of the temperature cycle. When it reaches the contact surface with the upper and lower copper pillars, stress deformation occurs due to the different material properties of the two. It can be speculated that if the simulation is continued, fatigue cracking will occur at the interface between the solder joint and the upper and lower copper pillars, which will cause the chip to fail.
In order to more clearly analyze the stress and strain of the solder joint under the thermal cycling load, a node in the middle of the solder joint is now selected as the research object, and the stress and strain curve is drawn for analysis. As shown in Figure 7, the curve of the equivalent shear stress of the joint at the middle of the solder joint over time. In the figure, the horizontal axis represents time, and the vertical axis represents the numerical value of the stress change of the node. It can be seen that the equivalent shear stress of the node changes periodically with the progress of the thermal cycle.
It can be seen from Fig. 8 that the viscoplastic strain energy density of the solder joint gradually increases with time, and the increase in each cycle is basically the same.
The stress-strain hysteresis curve of the internal node of the solder joint is shown in Figure 9, where the horizontal axis represents the equivalent shear strain of the internal node of the solder joint and the vertical axis represents the equivalent shear stress of the node. It can be seen from the figure that as the temperature cyclic load is loaded, the stress-strain hysteresis curve moves to the right, and the interior of the solder joint is undergoing cumulative plastic deformation.
2.6. Fatigue life prediction
In the case of loading thermal cycle load, the stress and strain behavior of solder joints is very complicated, and factors such as time, temperature, and solder all affect the performance of solder joints. In general, plastic strain is the root cause of cracking of solder joints until failure. Therefore, we use the strain fatigue model Manson-Coffin to predict solder joint life.
Fifties of last century, the relationship equation
proposed in the famous paper published by Coffin and Manson [8, 9]. It relates the fatigue life to the magnitude of the inelastic strain applied. The index β is found to be very common in pure metallic materials and very close to 2, it has nothing to do with their microstructure. When the plastic strain amplitude is large, this law applies to the definition of low cycle fatigue state (LCF) [10]. In the low cycle thermal cycle, the fatigue life (
) and the nonlinear strain amplitude (
) have the following relationship regardless of the residence time:
![](data:image/png;base64,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)
In the formula, is the fatigue life, C and β are the constant numbers of the sample, and
is the inelastic strain amplitude.
Above we introduced a method for predicting thermal fatigue life—C-M empirical equation based on strain range. However, since this equation only deals with the influence of the magnitude of the strain amplitude on the thermal fatigue life, it does not take into account the influence of temperature on it, thus reducing the credibility of its predicted life, so there are limitations. In order to solve this problem and make the results of life prediction more accurate, Engel-Maier's C-M correction equation becomes a more accurate one of many derivative equations:
![](data:image/png;base64,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)
Among them,
represents the equivalent plastic shear strain range
, and
represents the fatigue toughness coefficient (take 0.325) [11]. C stands for the fatigue toughness index, which can be determined by the following formula.
![](data:image/png;base64,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)
In the formula, Tm is the arithmetic mean of high and low temperatures, and f is the number of loads per unit time. The Engel-Maier correction formula not only reduces the number of model parameters, but also simplifies its structure. Because of the influence of temperature, the result of this formula is relatively accurate. It is widely used in calculating the thermal fatigue life of solder joints.
Through the comparison and calculation of the strain range of each node in the central part of the solder joint by the ANSYS program, the node with the maximum strain range can be obtained. The equivalent plastic strain range of the node = 0.0082, and the plastic shear strain range = 1.42×10-2. The average temperature of the temperature cyclic loading load is Tm = (150-50)/2=50 °C, and each thermal cycle is 36 min. The temperature cycle frequency f=1.67cyc/h can be calculated and substituted into Equation (5), and it can be calculated C=-0.455, substituting the above data into Equation (4), the fatigue life of the silver tin solder joint can be calculated = 2166 weeks.