Die wear numerical analysis based on Archard’s model under stable deformation*

Jian-jun HU ，Tian-feng HOU

1College of Material Science and Engineering，Chongqing University of Technology，Chongqing 400054，China;2Mould Technology Chongqing Municipal Key Laboratory of Institutions of Higher Education，Chongqing 400054，China

1.Introduction

The forging die，which was widely used in the production of parts of cars and machines，had taken a quite important role in forging production.To evaluate the production efficiency and the cost of the final product，the life of dies was the important reason.The mechanism of die forging was quite complicated because die forging was in the continuous working state of mechanical load and thermal load，and it also had friction，wear，fatigue failure，heat exchange and plastic deformation in forging.The current situation shows that wear and deformation are the most common failure form［1］.Wear was the crucial factor that influences the life of dies in extrusion forming，especially in RHCM(Rapid Heat Cycle Molding)，over 70%dies failure was due to wear according to the study.That＇s the reason that reducing the wear became one of the main concerns.

Wear could not only damage surface quality of dies，but also change the size of impression，which all above influence the life of dies badly.The designers made many ways to increase the life of hot extrusion die，such as improving molding process，selecting advanced material of dies and hardening the case of die，but all failed.The mould design can be better directly if the relationship could be built between process parameters and die wear［2］.

After all these years，there were a large number of studies conducted in the tribology field for the system analysis theory and method of abrasion mechanism and tribology as well as microscopic analysis of abrasion surface，etc.But most abrasion research method was carried out for experimental study.Such method for experimental study consumes a great deal of time，manpower，resources and money.According to the complexity and different operating conditions of actual tribology system，the test result can not be used well in system design and actual engineering applications，such as abrasion life prediction，abrasion dynamic monitoring and abrasive resistance design etc.［3］.

Whereas，the numerical simulation technique which provided a new method for tribology research，may made it up.The numeric emulation technique shall be used for tribology system study to establish simulation model based on the analysis and research for tribology system，and the model shall be improved and ameliorated by adopting the computer to increase the efficiency of tribology research and the accuracy of tribology system characteristic prediction obviously.

For numeric emulation analysis of abrasion，some foreign scholars carried out a lot of researches on abrasion model，abrasion prediction and abrasion reduction.Painter and other people simulated the process of mould abrasion caused by hot extrusion with finite element software［4］.Lee and Im conducted the research on abrasion and elastic deformation of mould by using finite element technique［5］.Lee and Jou analyzed the abrasion of forging mould by adopting numerical simulation analysis［6］.Wang Lei from materia(material)institute of Jiangsu university in China calculated the transient temperature，pressure and velocity field of each node at the forming stage by extrusion of mould based on corrected Archard abrasion theory，as to calculate the cavity abrasion of cone extrusion mould and arc extrusion mould［7］.Zhou jie from Chongqing University simulated and analyzed the effect regulation to mould abrasion after one-off formation of model rigidity，initial temperature and lubrication condition by adopting Archard abrasion model［2］.Hereafter a discussion is carried out on the abrasion mechanism of mould grinding abrasion to seek for the abrasion regulation of mould grinding abrasion by adopting numerical simulation method.

2.Archard abrasion model

Abrasion failure of mould refers to the friction loss between working position of mould and materials to be processed.It is divided into normal abrasion failure and abnormal abrasion failure.The abrasion of abrasive grain refers to the external hard particle or the phenomena that the pumps make the surface material fall off while rubbing the pumps，the definition in tribology terms prepared by the Organization for E-conomic Co-operation and Development(OECD)is“the abrasion due to the material transition caused by the action of hard particle or hard micro pumps”.The popular abrasion mechanism of abrasive grain at present includes:①microcosmic cutting mechanism;②abrasion mechanism due to the breaking caused by plastic deformation;③microcosmic brittle failure abrasion mechanism.During the grinding abrasion in actual mining，a combining action of several mechanisms will work，but one of them will act as the main action.As the grinding abrasion will be affected by may factors such as interior tissue and performance of material as well as abrasion external conditions，where，the main mechanism of abrasion sometimes varies along with the changed affecting factors［8］.

Some foreign scholars had proposed a great many abrasion models，Rabinowicz established the abrasion model for the abrasive grain.The abrasive rate obtained from the model is one to two orders of magnitude higher than the actual one，and cannot explain the influence of the dimension of the abrasive grain.Staffan Jacobson established the bidimensional grinding abrasion statistics model［9］which is only generally applicable to the pure cutting process without involving the influence by the formation of the plastic deformation wedge and plastic deformation ridge to the abrasive process and failed to consider the condition that many abrasive grain participate in the abrasive condition under the multiple contact conditions.It cannot reflect the actual situation［10］.

From 1953，the Archard theory has been widely used to analysis the abrasion of the match tool.It has been effectively used in the calculation of the mold grinding abrasion.The Archard model was proposed，developed and completed firstly by Holm.Initially it was the formula derived from analyzing the adhesive wear mechanism.However，it was proved by the subsequent experiences that it has the similar effect to the other abrasive mode.Thereafter，many of the establishments’models are usually concerning with this mode.The Archard introduced the concept of the actual contact area into the derivation［8］.

Archard theoretical model，as shown in Figure 1，the tangency of the two nominal smooth surfaces occurs in the higher peak unit，shown in Figure 1(a).Due to the influence of the partial concentrated stress，plastic deformation occurs on the contact area.What is shown in Figure 1(b)is the situation while two peak units contact each other，and that shown in Figure 1(c)is the relative movement of the interface due to the contact，and abrasion occurs on the peak units，and the generation of the abrasive dust.

Figure 1.Archard wear calculation model

The conventional Archard abrasion model has already been adopted to predict the abrasion of the mold.The abrasion loss is proportional to the mortality factor abrasive coefficient，the apparent pressure of the mold and the relative move quantity between the mold and workpieces，while it is inversely proportional to the hardness of the mold.Namely Archard abrasion prediction model can be expressed as:

Where，K is abrasive coefficient，x is the sliding length，p is apparent pressure，H is hardness of the tool.

3.Mold abrasion analysis under sustained deformation condition

As shown in Figure 2，it is the mechanism of the mold surface deterioration during the extrusion process，the sliding distance in random position，lij，can be expressed as:

Figure 2.The abrasion mechanism during extrusion process

During time Δtj(Δtj)，the abrasion loss at random positions could be expressed with the Archard abrasion model as:

Here T was temperature.

The ultimate abrasion loss after an extrusion accomplished could be expressed as:

Where n is the step number used during the simulation accomplishment to accomplish the simulation.

Under such premise，when n approaches infinity，as the continuous regime，the Archard abrasion model can be expressed as:

Where，W is the abrasion loss，P is the positive pressure of the mold surface，V is sliding speed，H is initial hardness of the mold(HRC)，as for steel，K is the relevant constant to the material characteristics，as for metal［5］，a=b=1，c=2，K=2 ×10-5.

When the deformation zone and the speed are stable，F(xiàn)ormula(5)can be written as:

In identical deformation time，for K，p，v and time are all constant masses，thus under the condition that the sustained condition has been formed，it can be assumed that abrasion loss W is proportional to the function(1/H2).

4.Simulation of the mold abrasion based on the Archard theory

As shown in Figure 3，it is a backward extrusion case，materials AISI-1010-1010 of workpieces.Materials of the mold is AISI-H-13，the temperature is normal，speed of the upper mold is 25.4 mm/s，distance of travel of the mold is 38.1 mm，K is taken as 0.000 002，friction factor m is taken as 0.1.

Figure 3.Inverted extrusion finite element model

Table 1 was the maximum abrasive depth of the male mold with initial hardness range from HRC 45-65，F(xiàn)igure 4 indicated the relationship between the increase of the abrasive depth of the male mold along with and the changing of the hardness.It can be observed that the maximum abrasive depth decreases along with the increase of the initial hardness of the materials.When the initial hardness is HRC45，the maximum depth after one-time forming is 1 188.72 ×10-6mm;while the initial hardness increased to HRC 65，the maximum depth is only 568.96 ×10-6mm，the antifraying ability has been increased by 2 times or higher.Figure 5(which was calculated by DEFORM-3D software)shows the distributing situation of the surface deterioration of the male mould when the initial hardness is HRC65.

Figure 4.Hardness with maximum abrasive depth

Matching the maximum abrasive depth of the male mould with the same hardness with the function(1 000/H2)using the method of least squares，the curve after matching is shown in Figure 6;it can be observed that it goes with the linear relation.Coincidentally，under such material and process conditions，the Adj.R-Square of line fitting is exactly 1.

Figure 5.Maximum abrasive depth of punch(HRC55)

Figure 6.Maximum abrasive depth with(1 000/H2)

5.Conclusion

Using Archard theory model to predict the numerical simulation of die wear，through theoretical analysis and numerical simulation，the following conclusions can be drawn.

1)Based on the theory of Archard wear，using the finite element analysis software to calculate the wear of cavity of extrusion die，and provide the basis of the wear design of die cavity.

2)The maximum wear depth of die decreases with the increasing of initial hardness of die.

3)Under the stability condition，in the deformation zone the maximum wear depth of die is in direct ratio with function(1/H2)

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