Cyclic Biaxial Stress Measurement Method Using the Grain Growth Direction in Electrodeposited Copper Foil
© The Author(s) 2010
Received: 28 December 2009
Accepted: 11 April 2010
Published: 17 May 2010
A method that uses grain growth direction in electrodeposited copper foil to measure cyclic biaxial stress is examined in this paper. The grain growth direction is measured by image processing software after a cyclic loading test for various biaxial stress ratios is carried out. Since the grain growth occurs in two directions and its directions correspond closely with the direction of maximum shearing stress when the biaxial stress ratio is negative, the principal stress can be measured using Mohr's stress circle. On the other hand, when the biaxial stress ratio is positive, above-mentioned feature does not occur. Therefore, the first principal stress can be measured based on the grain growth density. The number of grains necessary to measure the biaxial stress is estimated by a statistical approach.
The copper electroplating method is used to measure cyclic stress that causes metal fatigue [1–3]. If copper foil adhered to a machine element is subjected to repeated loads, grain growth occurs in the copper foil. Since the grain growth density is controlled by the maximum shearing stress and the number of cycles, the maximum shearing stress can be measured based on the grain growth density in the prescribed number of cycles . This method has the advantage of detecting stress in microscopic regions like the stress concentration region. Moreover, this method can be easily applied to rotating machines and machine elements in sealed casings, since it does not need an output line like an electrical resistance strain gauge.
Since the principal stresses that are important for evaluating metal fatigue cannot be detected by this method, a new method using copper foil with circular holes has been developed [4, 5]. However, this new method is somewhat complex, because the grain growth length at hole edges as well as the grain growth density in the copper foil must be measured. This also means that two kinds of copper foils (foil with and without circular holes) are necessary for the principal stress measurement.
From the above viewpoint, we examined the principal stress measurement using only one piece of foil without circular holes. To do this, we focused on the grain growth direction, since the growth direction of an individual grain is expected to correspond closely with the direction of maximum shearing stress. The principal stress measurement becomes possible using this feature as described in the next chapter. First, we proposed the principal stress measurement method based on the grain growth direction. Second, we investigated the relative frequency distribution of the grain growth direction for various biaxial stress conditions. Finally, the number of grains necessary to measure the principal stress was estimated by regarding the relative frequency distribution as the normal distribution.
2. Biaxial Stress Measurement Method
3. Experimental Procedures
3.1. Test Specimen and Testing Machine
A copper foil was obtained as follows. A stainless steel plate (200 mm 100 mm 1 mm) was electroplated with copper sulfate solution . Since the stainless steel plate is polished by buffing before plating, the deposited layer can easily strip from the stainless steel plate. This deposited layer is called a copper foil. All subsequent experiments were carried out by cutting this single foil to small pieces. The copper foil was about 20 m thick and the initial grain size was about 1 m . This grain size is considerably smaller than the grown grain size.
Mechanical properties of Ti-6Al-4V alloy.
Proof stress [MPa]
Tensile strength [MPa]
3.2. Experimental Procedure
4. Results and Discussion
4.1. Statistical Distribution of the Grain Growth Direction
4.2. Biaxial Stress Measurement Using the Grain Growth Direction
4.3. Estimation of the Number of Grains Necessary to Measure the Biaxial Stress
Since this method has the advantage of enabling measurements of the stress in a microscopic region, it is preferable to reduce the number of measured grains as much as possible. The number of grains necessary to determine the sign of biaxial stress ratio is only about 50, since the feature shown in Figure 9 is the same within the range from 50 to 150. Therefore, we pay attention to the number of grains necessary to measure the biaxial stress ratio. Namely, necessary to keep prescribed accuracy in the stress measurement can be statistically estimated.
We examined a method that uses the growth direction of grains in copper foil to measure cyclic biaxial stress. The number of grains necessary to measure the biaxial stress was also estimated statistically.
When the biaxial stress ratio is negative, peaks of the relative frequency distribution of the grain growth direction corresponded well with the direction of maximum shearing stress, and the interval from one peak to another peak was almost 9 .
The above-mentioned features are not recognized when the biaxial stress ratio is positive. Therefore, the sign of biaxial stress ratio is determined by using these features.
The principal stress was obtained with Mohr's stress circle and the peak of the sin curve obtained by approximating the relative frequency distribution when the biaxial stress ratio is negative.
The grain growth direction within the range of 4 from one peak of the distribution followed the normal distribution. Therefore, the number of grains necessary for the principal stress measurement could be estimated to the demanded accuracy.
Since this method can measure the principal stress with only one piece of foil, it is more efficient than conventional methods.
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