Wire & Cable Technology International - January/February 2008 - (Page 62)

Tips From WireDrawing 101® by: Dr. Roger N. Wright Roger N. Wright, Inc. 12 Maria Court Rexford, NY 12148 USA E-mail: wrighr@rpi.edu www.rnwinc.com Most basic engineering analyses of drawing involve a central role of the wire strength or flow stress. The parameters most important to the strength are the strain since the last anneal, the temperature and the strain rate. In my opinion, strain rate is the least appreciated of these factors, hence motivation for this month’s column. The average strain rate in a drawing pass is simply the strain of the pass divided by the length of time the wire takes to go through the deformation zone in the die. The time to go through the deformation zone is the length of the deformation zone, L, divided by the average drawing speed, V. Strictly speaking, V = V1(1 - ½ r), where V1 is the drawing speed at the die exit and where r is the drawing pass reduction (in decimal form). In any case, the average strain rate, έ, can be expressed as έ = Vφ ln [(1/(1-r)]/L, where φ is the redundant strain factor, with φ ln [(1/(1-r)] being the total strain of the drawing pass. The deformation zone length, L, can be converted to an expression, (d0–d1)/[2 tan α], where α is the die semi-angle, and where d0 and d1 are respective wire diameters, before and after the pass. Fortunately, the redundant work factor can be approximated with the use of Δ, and a fairly comprehensive formula for wire drawing strain rate can be: έ = [(6.4) V tan2α /(d0–d1)] [(1/Δ)+ 0.28]. We have often used Δ to describe deformation zone geometry, and Δ can be expressed as (4tan α)/ ln[(1/(1-r)]. For practical purposes, the formula seen above can be greatly simplified, and for typical die angles and reductions, the strain rates in drawing can be roughly estimated by the relation έ = (0.04)V/(d0–d1). Now this means that a reduction from 2 to 1.8 mm at a speed of 3 mps would involve an average strain rate of 6 x 102 per second. Similarly, a reduction from 0.2 to 0.18 mm at a speed of 30 mps would involve an average strain rate of 6 x 104 per second, and so on. In general, it is common for wire drawing strain rates to be in the 103 to 104 s-1 range. Of course, laboratory drawing and drawing in tandem with certain coating or cleaning operations, at slow speeds of say 0.5 mps, will involve strain rates as low as 102 per second. In comparison to most mechanical testing strain rates, wire drawing strain rates are quite high. For example, routine tensile testing is often undertaken in the strain rate range of 10-3 per second, six or seven orders of magnitude below much of the commercial wire drawing strain rate range. This difference in strain rate can have a major impact on Strain Rate the wire strength, and it can be misleading to use routine tensile data to make drawing stress calculations for higher speed drawing operations. For nonferrous drawing, high strain rate strengths and flow stresses can be rather reliably estimated. Typically, one uses the relation σ = C(έ)m, where m is the strain rate exponent (about 0.012 for copper, and 0.0155 for aluminum, in the drawing temperature range), and where C is a strength coefficient that can be evaluated by a normal tensile test by noting the strain rate of the test and the yield strength. Therefore, for the case of copper, one could expect a flow stress increase of (107)0.012 or about 25% over a seven-orderof-magnitude change in strain rate. Of course, such changes in strain rate and processing operations usually involve substantial temperature changes as well. The increased deformation temperature typically associated with the higher strain rates generally lowers strength in nonferrous metals, offsetting the increase in flow stress intrinsically associated with the strain rate change itself. For steel, the situation is much more complicated. For lowcarbon steel, at room temperature, the value of m is about 0.07, and flow stress increases considerably with strain rate. However, at temperatures above room temperature, but in the drawing temperature range, dynamic aging occurs. When dynamic aging is present, the flow stress actually increases with decreasing strain rate (sometimes called the “anomalous strain rate effect”). Now the temperature, Tda, at which dynamic aging is most potent is itself a function of strain rate, and for low carbon steel may be approximated (in the drawing temperature range) by the following relation: Tda = 600 έ .04, where Tda is in ºK and strain rate is per second. For the case of low-carbon steel at a strain of 5%, the maximum dynamic-strain-rate enhanced flow stress is about 500 MPa (75 ksi) for the pertinent strain rate. The author has recently presented a review of aging phenomena in ferrous drawing (2007 Conference Proceedings, Wire Association International, pp. 258-269). So…, this is another complex topic where awareness is the most useful application. Nonferrous drawers should be aware that drawing strain rates involve a few tens of percent increase in strength over room temperature tensile test properties. Ferrous drawers should be aware that dynamic strain rate effects are active at hundreds of degrees Celsius for wire drawing strain rates, while being more in the boiling water range for ordinary tensile test strain rates. Good luck!!!! WCTI The WireDrawing 101® short course, presented and developed by Roger N. Wright, Inc., and Wire & Cable Technology International magazine, is the comprehensive two-day course that teaches the fundamentals of wire drawing to manufacturers of ferrous and nonferrous wire. WireDrawing 101 features a unique handbook, with practical process design and trouble-shooting exercises suitable for work-a-day formats and continuing study. The next offering will be June 10-11, 2008 in Pittsburgh, PA, USA. www.wiretech.com / www.rnwinc.com 62 Wire & Cable Technology International/January 2008 http://www.rnwinc.com http://www.wiretech.com http://www.rnwinc.com

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Wire & Cable Technology International - January/February 2008 Editorial Wire & Cable Events Industry News Global Economy Drives Specialty Cable Demand Corporate News Change is Tough! Top Products of 2007 New Magnesium Hydroxides Enabling Low-Smoke Cable Compounds Straight From the Show - IWCS Conference™ A History of Long-Term Thinking Ensures a Pioneering Spirit Expediency of Roller Dies Application in Wire Drawing - Part 1 WireDrawing 101 Strain Rate Transforming Our Ideas Into Your Success Straight From The Show - Wire Southeast ASIA 2007 Capstans, Dancers, Accumulators Roundup Spotlight On Quality Control Pioneering Virtual Technology for Extrusion Electrically Heated Furnace Cuts Energy Costs/Reduces Carbon Footprint Machinery Accessories Materials Polymer Developments in the Cables Industry Wire & Connector Top Products of 2007 Just Load, Click and Print Superior Flame Resistance for Minimal Smoke, CO & Acid Gas High-Flex Round Cable Added to On-Line Design Tools Failed Bridge Cables Replaced With Smaller, Stronger Ones Advertisers Index Classified Advertising Internet Spotlight Editorial Index

Wire & Cable Technology International - January/February 2008

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