Modeling of Materials for Sports Equipment 1 introduction

1.3.1 Application of Modeling: Assessing Hardness Around a
Weld
A relatively simple application of the modeling principles is provided by
the variation in hardness around a fusion weld in a 5xxx series AlMg
alloy, as may occur in the welding of bicycle tubes. As noted earlier, the
strengthening mechanisms in this alloy are solid solution strengthening
(from the Mg alloying), grain size, and work hardening. During fusion
welding, the base metal under the heat source (electric arc) is melted,
with heat being conducted into the base metal raising the temperature of
the adjacent material from ambient (far-field) to the melting temperature
(at the edge of the weld pool). Exposure of the base metal to elevated
temperatures can cause loss of work hardening by recovery (low temperatures), recrystallization, grain growth, and, finally, dissolution of intermetallic particles (highest temperatures). These processes are driven by the stored energy and grain size in the base metal (determined by the amount of cold work) and the intermetallic particles (determined by alloy preparation). The temperatures at which each process commences can be determined theoretically or practically and the rates for each temperature are calculated so that the extent of each process for a given time step at any temperature can be determined. As each process proceeds, the driving force is consumed and is, thus, modified for the next stage, as whereXRis the fraction recrystallized, QR0is the initial activation barrierfor recrystallization, QRis the current activation barrier for recrystallization, and Cis the constant.Welding uses a moving heat source and, therefore, the thermal fieldhas to be modeled using FE methods with a mesh that is finer close to theweld line, but gets coarser further away (Fig. 1.5) without loss of precision. This then gives the transient heating and cooling cycle for a givenweld heat input (Fig.1.6) that is used to give the extents of recovery,recrystallization, grain growth, and intermetallic dissolution which arethen combined to give the alloy strength (σ