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Validation and application of a screw method for strain measurement in bulk metal forming S J Yuan*, J Zhang, and Z B He Materials Science and Engineering School, Harbin Institute of Technology, Harbin, People’s Republic of China The manuscript was received on 2 October 2006 and was accepted after revision for publication on 21 June 2007. DOI: 10.1243/03093247JSA280
Abstract: A new method for measurement of plastic strain inside a deforming body is advanced and validated through a simple cylinder upsetting experiment. It is also applied to a ring for demonstrating this method in a ring compression test. The experimental results and numerical simulation show good agreement. In contrast with other physical modelling methods, this method utilizes the real metal for a sensor and workpiece, rather than using substitute materials, and can observe and measure material flow and plastic strain inside the specimen without splitting it before deformation. It can be used to study material flow and to predict strain distribution in general bulk metal-forming processes such as upsetting, extrusion, and die forging. It is also useful for verification of the numerical simulation methods when the material model and the processing parameters were uncertain and/or not easily verified. Keywords: strain measurement, bulk metal forming, physical modelling, numerical simulation
1 INTRODUCTION Numerical simulation is a powerful method for predicting the metal-forming process and optimizing the processing parameters. However, in practical bulk metal processes, especially in situations with a complicated workpiece geometry, when heat transfer is involved, with complex friction or lubrication conditions, for an uncertain material model, etc., the current commercial software and in-house codes could not provide sufficient accurate and credible results. Therefore, physical modelling is still an important means for obtaining certain experimental data, at least for the validation of numerical simulation results. Physical modelling is frequently used to investigate material flow in bulk metal forming. Generally, a soft material is chosen as a substitute for real workpiece metal. Plasticine [1–5] is a well-known physical modelling material. It can be repeatedly used to predict the forming behaviour and strain * Corresponding author: Materials Science and Engineering School, Harbin Institute of Technology, Room C608-1, Apartment A10, Harbin, Heilongjiang, 150001, People’s Republic of China. email:
[email protected]
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distribution of some complicated parts, with low cost. Photoplasticity materials [6–8] are also widely used in physical modelling. The photo effect of poly(methyl methacrylate) under stress is used to obtain measurements of the strain and stress inside a deforming body. Physical modelling methods introduce inevitable errors, owing to the property difference between the real material and the substitute material and the different workpiece–tool interfacial conditions [5, 9]. It is difficult to investigate the material deformation inside the deforming body because of the opacity and the high strength of metals. The mesh grid method [10–14] is often applied to measure the strain distribution in sheet metal forming. It can also be applied to bulk metal forming such as cylinder upsetting, but it is necessary to split the workpiece and to scribe a grid on the split section surface to study the deformation. A major problem with this method is that the stress state of the workpiece is then significantly altered. In this paper a new method called the screw method is advanced to investigate metal plastic strain inside a deforming body, as demonstrated in Fig. 1. A threaded hole was machined in the real metal specimen, and a bolt of the same material was J. Strain Analysis Vol. 42
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Fig. 2 Diagrammatic drawing of the cylinders (all the dimensions are in millimetres)
Fig. 1 Schematic diagram of the screw method: (a) initial section; (b) deformed section
screwed into the hole. This composite specimen was compressed and then sectioned along the midsection of the bolt. The deformed screw interface can be observed and measured on the section to investigate the material flow and plastic strain distribution inside the deformed body.
2 VALIDATION OF THE SCREW METHOD IN A CYLINDER UPSETTING EXPERIMENT Two aluminium alloy 2024 cylinder specimens were prepared, as shown in Figs 2 and 3(a). The initial diameter was 16 mm and the initial height was 10 mm. At different positions, a bolt hole was drilled and tapped with an M4 thread on each cylinder. Then two anodized bolts (Fig. 3(b)) of the same material were screwed into the holes. Each cylinder was heated to 400 °C with a perfect cylinder (without a bolt inside) of the same dimension and compressed to a height of 7.4 mm simultaneously. Figures 3(c) and (d) show the two pairs of cylinder after deformation. The deformed shapes of the two pairs of cylinder are identical after deformation under the same experimental parameters and equal height reductions. The J. Strain Analysis Vol. 42
cylinders with a bolt inside have exactly balanced profiles after deformation as do the perfect cylinders, which means that the defects caused by the implanted bolt are not great enough to influence the stress state inside the cylinders nor to result in unbalanced deformed shapes. The compressed cylinders with a bolt inside were sectioned along the middle section of the bolts. Sections with deformed screw interfaces were obtained as shown in Fig. 3(e); as can be seen, there are two visible screw lines on the section. The oxide film on the bolts generated by an anodizing treatment reduced the welding effect of aluminium alloy under high temperatures and stresses and allowed ease of interface identification. Therefore the screw interfaces can be easily identified through a microscope. With an ocular micrometer, the coordinates of the vertices on the screw interface line could be measured. The initial screw pitch (0.7 mm) was small, and so the screw line between adjacent vertices was assumed to retain its linearity after compressive deformation. The deformed screw lines can be obtained by connecting the measured vertices together. Numerical simulation of this cylinder upsetting model was carried out by the general finite element method software DEFORM 2D (Fig. 4(a)). Here a cylinder with the same dimensions was used without the inside cut profiles, i.e. the imperfection caused by the bolts inside the cylinder was ignored. An ideal rigid–plastic model with a flow stress of 87 MPa was defined in the simulation for the aluminium alloy 2024. Considering the hot-forging condition, the rough aluminium–steel interface and lack of lubrication, a JSA280 © IMechE 2007
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Fig. 3 Photograph of the cylinder specimen: (a) initial cylinders; (b) anodized bolt; (c) deformed cylinders (case 1); (d) deformed cylinders (case 2); (e) screw interface with two visible screw lines
friction factor of 0.4 was chosen in the simulation. Other conditions, such as the ram speed and temperature, were assigned the same values as those in the experiment. The dotted lines in the initial step (i.e. step 0) in Fig. 4(a) are the nodal points on the screw lines of the corresponding experimental cylinder sections. These nodal points can be tracked in the simulation. Figure 4(a) also shows the final step (i.e. step 52) with a specimen height of 7.4 mm, and JSA280 © IMechE 2007
the dotted lines represent points on the initial screw lines. The dotted lines in the numerical simulation as well as the screw lines in the experiment can be used to track points inside the deforming specimen. Figure 4(b) shows the screw lines for the same coordinates, in which the coordinate lines represent experimental results while the dotted lines represent the simulation tracking points. Both the predicted deformation profile and the experimentally J. Strain Analysis Vol. 42
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Fig. 3 (Continued)
determined coordinates of the screw lines generally coincide. The deformed screw lines can be used to study the material flow behaviour inside the cylinder. In order to calculate the axial strain (i.e. the Y strain) on the screw lines, a short length of the screw lines was analysed as shown in Fig. 5. The area defined by ABCD can be taken as a strain infinitesimal; therefore the Y strain of P (the centre of ABCD) can be n expressed as
A
|y
B
−y | n+1 n−1 (1) Dy 0 in which Dy is the initial screw pitch, 0.7 mm. 0 Equation (1) is used to calculate the Y strain of four screw lines and compare with the simulation results in Fig. 6. The Y strain of the four screw lines of the experimental results and the simulation results are well correlated with respect to both the values and the trends. e =ln y
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3 APPLICATION OF THE SCREW METHOD IN A RING COMPRESSION TEST The ring compression test is often taken as a benchmark experiment of the bulk metal-forming process to study the plastic deformation characteristics of certain materials and processing parameters. Here a ring compression test was taken as a demonstration of applying the screw method in general bulk metal forming. An aluminium alloy 2024 ring specimen was prepared with initial inner and outer diameters of 16 mm and 50 mm respectively and an initial height of 24 mm (Fig. 7). At different positions, four bolt holes were drilled with an M4 tap. Four anodized bolts of the same material were screwed into the holes. The composite specimen was compressed to a height of 14.9 mm at a temperature of 400 °C. The original and final compressed rings are presented in Fig. 8. JSA280 © IMechE 2007
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Fig. 4 Cylinder section with tracking points obtained by experiment and simulation: (a) numerical simulation of cylinder upsetting, showing initial and final steps; (b) comparison of experimental and simulation results
Fig. 5 Strain infinitesimal of screw line
Numerical simulation of this ring compression model was also carried out as the previous cylinder upsetting model, for the verification of the experimental results. Figure 9 shows the four axial screw lines (provided by the two axial bolts in Fig. 7), JSA280 © IMechE 2007
Fig. 6 Y strain comparisons of experimental results and numerical simulation J. Strain Analysis Vol. 42
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Fig. 7 Diagrammatic drawing of the ring specimen (all the dimensions are in millimetres)
denoted Z1, Z2, Z3, and Z4, obtained by experiment and simulation. The results show good agreement with respect to both the values and the trends. The four screw lines inside the ring can provide information about the metal flow. Obviously there is a flow interface between Z1 and Z2; material inside the flow interface flows to the inside, while material outside the flow interface flows outside. It can also be concluded that the material near the tool flows more slowly than the material far away from the tool because of the friction. Equation (1) is used to calculate the Y strain of the four axial screw lines and to compare with the simulation results in Fig. 10(a). The Y strain of the
Fig. 8 The initial ring (left) and the compressed ring (right)
Fig. 9 Ring section with tracking points obtained by experiment and simulation J. Strain Analysis Vol. 42
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element method software, but also because of the simple model of the cylinder upsetting and ring compression test introduced here. In practical bulk metal processes, especially in those situations with complicated workpiece geometry, when heat transfer is involved, under complex friction or lubrication conditions, for an uncertain material model, etc., the current commercial software or in-house codes could not provide sufficient accurate and credible results. Since the screw method utilizes the real metal for the sensor and workpiece and can be used in those complicated processing situations, it is also useful for verification of the numerical simulation methods while the processing parameters were uncertain and/or not easily verified. It is obvious that the screw method can be used as a new strain measurement method in bulk metal forming. To obtain reasonable results, the following points should be noted. 4.1 Bolt size
Fig. 10 Strain comparisons of experimental results and numerical simulation: (a) Y strain on axial screw lines; (b) X strain on radial screw lines
four screw lines of experimental results and simulation results are well correlated with respect to both the values and the trends. Similar to equation (1), the X strain (i.e. the radial strain) on the radial screw lines (provided by the two radial bolts in Fig. 7) can be calculated. Figure 10(b) shows the X strain on the radial screw lines of the experimental results and simulation results. The experimental and numerical results again are in good agreement.
4 DISCUSSION It should be noted that numerical simulation was applied in this paper for validation of the screw method, not only because of the powerful capability and high accuracy and efficiency of the finite JSA280 © IMechE 2007
It is advisable to use small bolts because a small pitch is better to improve the accuracy of strain measurement. However, difficulties may arise in drilling and tapping small holes in large test pieces. It is not appropriate to use this method when the test piece is so small that the bolt inside takes a large percentage of volume of the whole test piece, because this could make the defects inside change the stress state markedly and lead to an unbalanced shape of the final test piece. Figure 11 shows an example of a small cylinder with an axial bolt inside. Compared with the perfect cylinder, the deformed shape was largely influenced by the inside defects caused by the bolt. 4.2 Oxidation treatment An oxidation treatment of the bolts can reduce the metal welding effect under high stresses and temperatures. This is very important for the screw method. An oxidation treatment should be applied to bolts or the test specimen if necessary. Figure 12 shows the effect that the oxidation treatment has on the screw interface under the microscope. The interface with the oxidation treatment is clearly visible and measurable while the interface without the oxidation treatment is not easily identified because of the welding effect. 4.3 Stress state inside the specimen It should be mentioned that the compressive stress state is better for this method than the tensile stress state; i.e., if the bolts bear too much J. Strain Analysis Vol. 42
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Fig. 11 Comparison of a defect-influenced cylinder (left) and a perfect cylinder (right)
tensile stress, the accuracy of the strain measurement may decrease. As shown in Fig. 12, the screw line was deformed under compressive and tensile stresses, just as a spring. For the compressive stress case, the deformed screw line can be easily measured by microscope because the vertices are quite clearly located while, for the tensile stress case, the screw line becomes smooth and the vertices are quite hard to locate, which can decrease the accuracy of this method.
5 CONCLUSION
Fig. 12 Screw line interfaces of an aluminium alloy specimen: (a) without an oxidation treatment; (b) with an oxidation treatment J. Strain Analysis Vol. 42
The screw method has been verified in a cylinder upsetting experiment to observe and measure material flow behaviour and plastic strain. A ring compression test was carried out as a demonstration of applying the screw method in general bulk metalforming processes. The flow lines and strain distribution obtained by experiment have been compared with the numerical simulation results. The results are well correlated. In contrast with other physical modelling methods, this method utilizes the real metal for the sensor and workpiece rather than using substitute materials and can observe and measure material flow and plastic strain inside the specimen without splitting it before deformation. It can be used to study material flow and predict strain distribution in general bulk metal-forming processes such as upsetting, extrusion, and die forging. It is JSA280 © IMechE 2007
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Fig. 13 Screw lines under compressive stress and tensile stress
also useful for verification of the numerical simulation methods when the material model and the processing parameters were uncertain and/or not easily verified.
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ACKNOWLEDGEMENT This paper was financially supported by National Natural Science Foundation of China (Project 50525516), and the authors would like to take this opportunity to express their sincere appreciation for this support.
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