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– Peak TemperaturesomxopTTqYchueTT121c = specific heate = natural exponenth= workpiece thicknessq = power inputTm= melting temperatureTo= initial temperatureTp= peak temperatureux= traverse velocityY = distance from the fusion boundary at the workpiece surface= density
2000 # 43WeldingAnalysis –Heat Flow – Peak Temperatures•The peak temperatures are useful forEstimating heat affected zone size (HAZ)Showing effect of preheat on HAZ•The equation that gives the higher computed distance is the more accurate of the two•It is evident thatPreheating increases the size of the HAZHAZ size is proportional to the power input2000 # 44•A single full penetration weld pass is made on a thin steel plate using a power input of 3.75 kW, and welding speed 8 mm/s, resulting in a heat transfer efficiency of 85%. The material has a specific heat per unit volume c of 0.005 J/mm3-oCand thickness 5 mm. •If the ambient temperature is 30 oC, and the melting temperature of the material is 1600 oC, determine:a. the peak temperature at a distance of 1.0 mmfrom the weld fusion boundaryb. the heat affected zone size.WeldingAnalysis –Peak Temperatures – Example
2000 # 47b.WeldingAnalysis –Peak Temperatures – Solution2000 # 48WeldingAnalysis –Heat Flow – Cooling Rates•The cooling rates also affect theMicrostructure=Grain structure=Phases Mechanical properties•Knowledge of cooling rates is most important forMaterials that are polymorphic=Enable a variety of phases to be formede.g. steels•Less important when cooling rates are always highe.g. Al
2000 # 49WeldingAnalysis –Heat Flow – Cooling Rates•Cooling rates can be obtained by differentiating temperature equations with respect to time•Process is simplified by following assumptionsHighest cooling rates occur=Along line of motion of heat sourcei.e. y=z=0, and r=||=Behind heat sourcei.e. negative values ofor for 2000 # 50WeldingAnalysis –Heat Flow – Cooling Rates•This reduces the 3-d temperature distribution equation to the form:kqTTo22)(exp2rukrqTTxo•Differentiating with respect to tgivesdtdTtTdtdT
2000 # 51WeldingAnalysis –Heat Flow – Cooling Rates•There is no temperature change with time with respect to the moving coordinate system•ThusdtdTdtdT•Now since22kqTkqoTT22)(220TTqkkq20)(2TTqk2000 # 52WeldingAnalysis –Heat Flow – Cooling Rates•Using the chain rule, we havexudtdxdxddtd