Investigations on the Predictability of Coining Stainless Steel AISI 410 S.J.Grobbink * , G.Klaseboer * , J.Post * and J.Huetink † * Philips CL/AT, P.O. Box 20100, 9200 CA Drachten, The Netherlands † University of Twente, Department of Mechanical Engineering, P.O. Box 217, 7500 AE Enschede, The Netherlands Abstract. Due to the increasing trend towards miniaturization, various industries demand the knowledge of materials forming on microscale. Forming has many advantages above machining such as high accuracy, low costs and strengthening by cold- working. However, a drawback of microforming is that it leads to problems caused by so-called size effects. A lot of research has been done on this topic, but only a minor part deals with the forming of high strength materials. In this study two channels with 0.25 mm width and 4.5 mm length are formed in stainless steel sheet AISI 410 with an initial sheet thickness 0.5 mm. The channels are formed by the coining process. The experiments have been repeated in which all dimensions are scaled down by a factor two, in order to check if size effects occur. Ring compression tests are used to determine a shear friction coefficient. A finite element model was build up and solved with MSC.Marc in order to gain a better understanding of the coining process. A size dependent material model known from literature and a conventional material model is used for the simulations. Both results are compared with the experimental results. Keywords: coining, stainless steel, microforming PACS: 81.20.Hy ; 02.70.Dh INTRODUCTION In the last few decades, the increasing interest on the microforming of metallic parts has resulted in a lot of scientific research on this topic [1]. The interest can be explained by the current trend towards miniaturization and the advantages that metal forming has in comparison to machining. The material strength increases because of the cold working, which is often a desired effect. Also, a good surface quality can be achieved and because of the low costs and the possibility to produce at high production rates, microforming is especially applicable for the manufacturing of microparts in mass production. Forming at micro-scale introduces new problems though, which are known as size effects. In [1], the similarity theorem is used to define size effects as differences in experimental results after scaling down tool and specimen geometry, strain rates and process forces. An increase in friction [2] and scatter [3] can be found in literature. The most indisputable size effect however is the decrease in flow stress after scaling down the specimen or feature size. The decreasing flow stress can be explained by the surface layer theory [1]. Work hardening is related to moving dislocations in the grain and the pile-up of dislocations near grain boundaries. For this purpose, surface grains are less restricted than grains inside the material. A decreasing specimen size leads to an increasing share of surface grains, which weakens the material. This theory is often used to include size effects when modeling the material behavior on a macroscopic scale [4, 5], as well as on a mesoscopic scale [6]. After decreasing the specimen size even further to a couple of grains, the flow stress increases again. This can be explained and modeled by strain gradient plasticity [7], which accounts for higher order effects in plastic strain. A strategy to predict microforming processes is presented by Messner and co-workers in [8]. The idea is to combine upsetting tests and ring compression tests to measure material behavior and friction, and their potential size dependency. Ring compression tests are a well-known method to measure the friction in bulk metal forming for given materials, lubricant and surface roughness [9, 10, 11, 12]. In [8], no size dependency was found for the friction. Material behavior was found to be size dependent though, and an improved material model led to an error decrease between the experimental and numerical results from 11% to 4%. Kim and co-workers investigated the influence of feature size and bulk deformation on the formability of micro- protrusions during the coining of stainless steel AISI 304 [13]. It was found that if the bulk material flow is not constrained, a significant increase in formability could be observed, which was also pointed out earlier by Ike [14].
Transcript
Investigations on the Predictability of Coining Stainless SteelAISI 410
S.J.Grobbink∗, G.Klaseboer∗, J.Post∗ and J.Huetink†
∗Philips CL/AT, P.O. Box 20100, 9200 CA Drachten, The Netherlands†University of Twente, Department of Mechanical Engineering, P.O. Box 217, 7500 AE Enschede, The
Netherlands
Abstract. Due to the increasing trend towards miniaturization, various industries demand the knowledge of materials formingon microscale. Forming has many advantages above machining such as high accuracy, low costs and strengthening by cold-working. However, a drawback of microforming is that it leads to problems caused by so-called size effects. A lot of researchhas been done on this topic, but only a minor part deals with the forming of high strength materials.
In this study two channels with 0.25 mm width and 4.5 mm length are formed in stainless steel sheet AISI 410 with aninitial sheet thickness 0.5 mm. The channels are formed by the coining process. The experiments have been repeated in whichall dimensions are scaled down by a factor two, in order to check if size effects occur. Ring compression tests are used todetermine a shear friction coefficient.
A finite element model was build up and solved with MSC.Marc in order to gain a better understanding of the coiningprocess. A size dependent material model known from literature and a conventional material model is used for the simulations.Both results are compared with the experimental results.
In the last few decades, the increasing interest on the microforming of metallic parts has resulted in a lot of scientificresearch on this topic [1]. The interest can be explained by the current trend towards miniaturization and the advantagesthat metal forming has in comparison to machining. The material strength increases because of the cold working, whichis often a desired effect. Also, a good surface quality can be achieved and because of the low costs and the possibilityto produce at high production rates, microforming is especially applicable for the manufacturing of microparts in massproduction.
Forming at micro-scale introduces new problems though, which are known as size effects. In [1], the similaritytheorem is used to define size effects as differences in experimental results after scaling down tool and specimengeometry, strain rates and process forces. An increase in friction [2] and scatter [3] can be found in literature. Themost indisputable size effect however is the decrease in flow stress after scaling down the specimen or feature size.
The decreasing flow stress can be explained by the surface layer theory [1]. Work hardening is related to movingdislocations in the grain and the pile-up of dislocations near grain boundaries. For this purpose, surface grains are lessrestricted than grains inside the material. A decreasing specimen size leads to an increasing share of surface grains,which weakens the material. This theory is often used to include size effects when modeling the material behavior ona macroscopic scale [4, 5], as well as on a mesoscopic scale [6]. After decreasing the specimen size even further to acouple of grains, the flow stress increases again. This can be explained and modeled by strain gradient plasticity [7],which accounts for higher order effects in plastic strain.
A strategy to predict microforming processes is presented by Messner and co-workers in [8]. The idea is tocombine upsetting tests and ring compression tests to measure material behavior and friction, and their potentialsize dependency. Ring compression tests are a well-known method to measure the friction in bulk metal forming forgiven materials, lubricant and surface roughness [9, 10, 11, 12]. In [8], no size dependency was found for the friction.Material behavior was found to be size dependent though, and an improved material model led to an error decreasebetween the experimental and numerical results from 11% to 4%.
Kim and co-workers investigated the influence of feature size and bulk deformation on the formability of micro-protrusions during the coining of stainless steel AISI 304 [13]. It was found that if the bulk material flow is notconstrained, a significant increase in formability could be observed, which was also pointed out earlier by Ike [14].
Kim also used an earlier developed material model [4], which was validated with known size effects from literature.To get a better understanding of the coining process, the finite element method is a low-cost and time-efficient
way to investigate the influence of parameters such as friction, material behavior and tool design. However, it is onlyapplicable for this purpose if the finite element model gives a good description of the process. That is, if there existsa good agreement between the experimental and numerical investigations. The focus in this study is therefore toinvestigate the predictability of the coining process on stainless steel by the finite element method.
To do so, two micro channels of 0.25 mm width are formed by experimental tests and numerical simulations. Thewidth and distance between the channels are scaled down in the experiments to see if size effects occur. The load-displacement curves according to the experiments and the simulations are compared. Also, the specimen geometryfrom the finite element analysis is compared with that of the experiments.
After presenting the experimental setup and the results of the friction measurement in the next section, the materialmodel is presented. Because of the simplicity and the broad applicability, the model from Kim [4] will be used in thispaper to include size effects in material behavior. Then, the finite element model is presented in the next chapter, afterwhich the experimental as well as the numerical results are presented. Finally, some concluding remarks are given inthe last section.
EXPERIMENTS
Experimental setup
For the experiments, specimens are cut by a laser from sheet metal with a thickness of 0.5 mm. The specimens havea width of 5 mm and a length of 12 mm and contain two holes in order to position the specimen in the die set. Duringthe coining, channels with a width of 0.25 mm and a length of 4.5 mm per channel are formed near and parallel toeach other in the specimen. The distance between the channels is 0.35 mm. The material flow was only constrainedin thickness direction, thus bulk deformation was allowed. The forming is done by pressing a tool, which is shapedas two teeth, in the specimen material up to a force of 4500 N. The tool is made from cemented carbide, which is asuitable tool material due to its wear resistance and stiffness. The Young’s modulus of the used cemented carbide is600 N/mm2.
After scaling down the width of the tool’s teeth and the distance between the teeth with a factor two, the experimentshave been repeated for a force up to 2250 N. The width and thickness of the specimen are also scaled down by surfacegrinding to have a geometrically equivalent experiment. From grain size measurements and hardness measurementsit could be concluded that the grinding has no effect on the material behavior. The length of the channels and thespecimen is not scaled down because of a plane strain assumption. The tool for the first series of experiments as wellas the tool for the second series of experiments are polished before the coining, to decrease the risk of tool fracture.The front views of the tool profiles are given in Figure 1.
The positioning of the specimen and the guidance of the tool is done in a die set, see Figure 2. The force is appliedby a Zwick Z20 tensile tester. All experiments are done at room temperature, and the load as well as the displacementon the upper side of the tool are measured during the coining. Also, deep drawing oil is used as lubrication and thetool speed has been 0.12 mm/min. Since the total tool displacement including the system’s stiffness is ±0.6 mm, thetool speed implies a test duration of about five minutes.
0.250 mm 0.125 mm
FIGURE 1. Front view of the tool profiles. Left: large tool. Right: small tool
specimen
gap to insert the tool
tool
FIGURE 2. Die set. Left: open. Right: assembled, and placed in the tensile tester
TABLE 1. Chemical composition of stainless steel AISI 410 (%)
C Mn Si P S Cr
AISI 410 0.15 1.00 1.00 0.040 0.030 11.50-13.00
Friction measurement
Friction in coining processes influences the material flow, the stresses in the tool and the necessary forces to form theprofile in the specimen. In the finite element model, the friction force is often modeled by a constant ratio between thefriction stress and the normal or shear stress. Measured ratios for metal-to-metal contact with liquid lubrication varyin literature from 0.04 [15] to 0.85 [16]. A better estimation is necessary to gain a realistic model for finite elementsimulations. Therefore, the friction is measured by ring compression tests.
Three rings of the specimen sheet material and with an inner and outer diameter of 0.75 mm and 1.5 mm respectivelyare flattened to half of the initial thickness. This is done by cemented carbide blocks, which have a surface roughnesscomparable to the surface roughness of the coining tools. To determine a shear friction coefficient, the flattening of thering is modeled in a finite element simulation after the experiments. The coefficient is varied until the resulted innerdiameter from the simulation agrees with the resulted inner diameter from the experiment. The result is a shear frictioncoefficient m of 0.47±0.06.
MATERIAL MODEL
The chemical composition of stainless steel AISI 410 is given in Table 1. Tensile tests have been done on AISI410 with a grain size d of 11.2 µm, 15.9 µm and 22.5 µm, all with a strain rate 0.004 s−1. The Young’s modulus E isdetermined to be 212,000 N/mm2 and the Poisson’s ratio ν is determined to be 0.35.
In the first part of the stress-strain curves, discontinuous yielding is observed. This is typical for low-carbon steel,and is implemented in the material model as a straight line. The Nadai equation is used to describe the relation betweenthe true plastic strain and the true stress for the remaining part of the curves:
σ =Cεn (1)
in which n is the strain hardening coefficient and C the strength coefficient. Results are presented in Table 2.Extrapolation with the Nadai equation to high strains showed a good agreement with results from tensile tests
with pre-rolled tensile bars. It is assumed that higher order size effects in plastic strain can be neglected for the useddimensions in the experiments, thus only the decreasing flow stress as a consequence of the surface layer theory isimplemented. To do so, the relation from [4] will be used to describe the material behavior:
σ (ε) = Mατ (ε)+
κ (ε)√d
β [4] (2)
which is the extended Hall-Petch equation where α en β are added as size dependent parameters, and α = β = 1for polycrystalline material. Then, the first part of this equation accounts for the friction stress to move individualdislocations in isolated grains. It contains the resolved shear stress τ , and an orientation factor M, which is an averagevalue of all the different orientations of the grains in polycrystalline material. According to [17], the orientation factorof body-centered cubic (bcc) crystals is in the same order as the orientation factor of face-centered cubic (fcc) crystals.It is therefore assumed that the bcc structure of the ferritic stainless steel AISI 410, has the same orientation factoras the determined values in [18] for the fcc structure of copper and aluminum. That is, M = 2.6. The second part ofequation (2) deals with dislocations which come across grain boundaries, while moving through the lattice. Obviously,this part is a function of the amount of grain boundaries, thus the grain size.
Also, an analysis regarding the lower bound values for α and β is given in [4], which is summarized as follows.Scaling down geometry leads to a decrease in work hardening, which can be explained by the surface layer theory.The decrease should then have a lower bound, that is, if the specimen of the geometry decreases to that of a singlegrain. No inner grain boundaries are then responsible for stress increasing, thus β can decrease to 0 for decreasingspecimen size. Also, shear in a single grain occurs if the resolved shear stress increases to a critical value, which canbe expressed by the normal stress times the Schmid-factor m. Since m has a maximum possible value of 0.5, the stressin a grain should be at least 2τ for plastic deformation, which leads to the lower bound Mα > 2 while implementingthe size effects.
To determine the resolved shear stress τ and the grain boundary resistance κ , a plastic strain range εi is defined withi the number of strains. Per strain, the Nadai equation is used to determine the stress σ
ji for every grain size d j, in
which j is the number of grain sizes. Since the tensile tests are done on polycrystalline material (α = 1,β = 1), thematerial behavior can be determined per strain increment by
minκi,τi
3
∑j=1
((Mτi +
κi√d j
)−σ
ji
)2
(3)
The extended Hall-Petch relation showed a good agreement with the Nadai curves and the tensile tests.The size effect can be explained by the surface layer theory, which indicates that the hardening coefficient decreases
due to an increasing part of the grains on the surface relative to the total number of grains. Therefore, α and β aredirectly influenced by the cross sectional area of the specimen, the cross sectional area of the grain and its ratio n2. Therelation between this ratio and the parameters α and β is determined through iterative procedures in [4] for tensile testson CuZn in [1]. Also, from the analysis and according to [4], it is speculated that the results are material independent.The results will therefore be used to determine α and β in the coin tests.
The specimens for the coin tests had an average grain size of 15.9 µm and are taken from sheet metal. The hardnessof these specimens was HV 0.1 154. Since the sheets are soft annealed after rolling, both elastic and plastic part of thematerial behavior is assumed to be isotropic.
The Hall-Petch equation is used to describe the material behavior for the finite element method, in which acomparison will be made between the results of a simulation with a polycrystalline material model and the resultsof a simulation with a size dependent material model. To determine α and β for the size dependent material model,the width w and the length l of the channels in the specimen are used to determine the parameter n:
n2 =wl
14 πd2
(4)
TABLE 2. Nadai constants for differ-ent grain sizes
FIGURE 3. Material modeling. Left: parameters α and β and its dependence on n [4]. Right: resulting material model for bothtools
Then, the results from [4] can be used. The size effect on the flow stress according to the theory can be observed bycomparing the resulting material behavior with the conventional material behavior(α = β = 1), see Figure 3.
FINITE ELEMENT MODEL
A finite element model has been build and solved with MSC.Marc to get a better understanding of the coiningprocess. For example, the material flow and the stresses in the tool during the coining and the influence of varyingparameters can be seen. Also, it can be investigated if the decrease in work hardening due to the small specimen sizeshould be included, by comparing the finite element results with a conventional material model and a size dependentmaterial model with the experimental results.
Since the global strain in the direction of the channels was much smaller than the strain in the other directions, theproblem has been modeled as plane-strain. Adaptive meshing was necessary to avoid unacceptable element penetrationand distortion in the large deformation areas. The specimen is split into two parts with a glued contact in between. Inthis way, it is possible to use adaptive meshing only on the part where large deformations and tool contact occur, toreduce the computational time. For the same reason, the number of elements is reduced by using the symmetric axis.6000 linear quad elements with an analytical contact definition have been used to model the adaptive meshing part ofthe specimen. Linear quad elements are also used for the tool, to account for elastic deformation of the tool.
From the finite element analysis it is observed that the normal stresses on the contact of the tool and the specimenduring the coining process are larger than the flow stress of the specimen material. Under these circumstances, a shearfriction coefficient gives a better approximation for the friction stresses than the Coulomb friction coefficient [19]. Thefriction is therefore modeled by a shear friction coefficient.
In the simulation, coining has been done until the local thickness of the specimen in the coin region is the same as inthe experiments. Then, the received geometry and the load-displacement curves can be compared with the experiments.
RESULTS
Experimental results
A significant force has been necessary to remove the specimen from the tool by hand. The two channels which areformed with the large tool are given in Figure 4. The global strain in the width direction of the specimen is 0.03, whilethe global strain in the direction of the channels is smaller than 0.001. This justifies the plane strain assumption. In thenext section the differences in geometry after the experiments with the small tool and the large tool are given.
FIGURE 4. Experimental results (large specimen). Left: top view of the coined channels. Right: close-up
Numerical results
A thermal mechanical finite element analysis is done to investigate the heat generation caused by friction and plasticdeformation during coining. From the results, it can be concluded that the generated heat diffuses immediately in thespecimen because of the small tool speed. The resulting temperatures in the specimen increase with less than 5 K,which will have a negligible effect on material behavior. Also, strain rates during the coining vary from 0.002 to 0.03s−1 in the specimen, which is in the order of the used strain rates in the tensile tests. It is assumed that the variation instain rates has a negligible effect on the results. Heat effects and strain rate effects are therefore not taken into accountin the material model.
Figure 5 gives the mesh of the large tool and specimen after coining. In the mesh a contour plot of the new yieldstress is given. Along the coined contour a lot of work hardening can be observed. On the right side of the tooth itcan also be seen that the specimen material is adjacent to the tool. On the left side of the tooth, an angle is originatedbetween the specimen material flow and the tool. Nevertheless, contact occurs again due to the curvature in the tool.In the next section the results will be compared with the results from the experiments.
Comparison between the experimental and numerical results
Hardness measurements have been done on the cross section of the specimen. Since the relation between thehardness and the yield stress is known, the results can be compared with the new local yield stress according to
FIGURE 5. Experimental and numerical results (large specimen). Left: cross section of the specimen. Right: mesh and a contourplot of the new yield stress (N/mm2)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180
1000
2000
3000
4000
5000
Displacement of tool (mm)
To
ol f
orc
e (N
)
experimentFEM, without size effectFEM, with size effect
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090
500
1000
1500
2000
2500
Displacement of tool (mm)
To
ol f
orc
e (N
)
experimentFEM, without size effectFEM, with size effect
FIGURE 6. Load-displacement curves. Left: large tool. Right: small tool.
the simulation. A good agreement is found, which validates the material model for high strains as well as the materialflow in the finite element model.
The load-displacement curves according to the simulation and the experiments are compared in Figure 6. For afriction coefficient m = 0.5, which is in agreement with the results of the friction measurements, a simulation with theconventional material model shows an excellent agreement with the experiments, concerning coining with the largetool. Apparently, the material behavior can be described accurately with a conventional model for these experiments.For the small tool however, the conventional material model overestimates the required force if m = 0.5. This can bethe result of a decreasing flow stress due to the decreasing specimen size. The size dependent material model takesthis effect into account and gives a better result, but seems to underestimate the amount of decrease.
Also, the resulting geometry of the specimen after the simulation is in agreement with the experimental results,see Figure 5. Some dimensions are defined to quantify this. With t0 the initial thickness of the specimen, and t theremaining thickness of the specimen at the coin region, the coin-depth is defined as (t0− t)/t0. In the same way, therib-height is defined as r/t0, with r the height of the rib between the channels. Also, the mean inner and the mean outerangle can be compared. Because of the previous results, a conventional and a size dependent material model is chosenin the simulations for the large and small tool respectively. Both experimental and numerical results are presented inFigure 7.
From the experimental results, the size effect can be seen clearly by the greater rib-height and greater coin-depthafter coining with the small tool. However, the simulation overestimates the rib-height. Concerning the angles, no cleardifferences can be observed. It is in accordance with the simulations though, that a decrease in flow stress does notinfluence these angles. It can also be seen from the angles that the specimen material is adjacent to the tool at the side
t0 tr
coin depth t0−tt0
rib height rt0
γ η
inner angle γ outer angle η
FIGURE 7. A comparison of the geometry, according to the experimental and the numerical results. Left: coin depths and ribheights. Right: angles
of the rib, but not at the outer side, which is also in accordance with the simulations.
CONCLUSIONS AND RECOMMENDATIONS
It is possible to predict the coining process by the Lagrangian finite element method, using adaptive meshingfrequently. To get a better understanding, it is useful to perform experiments and friction measurements as well.
By comparing the load-displacement curves and the specimen geometries, coining with scaled down geometriesshows an increase in coin-depth. This can be recognized as a size effect. Assuming that the change in flow stress isthe cause of this difference, the material model from [4] gives an overestimation of this size effect for n = 75, and anunderestimation for n = 53.
Because of the high strain rates involved in the coining process, strain rate dependent behavior is recommended forcoining with larger tool speeds than in this study. Concerning the decrease in flow stress due to a decreasing featuresize, it is desired to implement this locally in material behavior. Strain gradient dependent material models could beuseful to describe this.
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