Finite Element Simulation of Multi-pass Laser ...

Finite Element Simulation of Multi-pass Laser Bending Process with Forced Cooling 1Ravi

Kant and 2S.N. Joshi

1Research

Scholar, Department of Mechanical Engineering, Indian Institute of Technology Guwahati, North Guwahati, Assam - 781039, INDIA e-mail – [email protected] 2Assistant Professor, Department of Mechanical Engineering, Indian Institute of Technology Guwahati, North Guwahati, Assam - 781039, INDIA e-mail – [email protected]

Abstract: Laser bending is an advanced manufacturing process that produces sheet metal curvature by means of laser beam irradiation over the worksheet surface. In the present work, numerical simulations of multi-pass laser bending process with forced cooling have been carried out by using finite element method (FEM). A 3-D nonlinear transient thermo-mechanical numerical model has been developed for multi-pass laser bending process under forced cooling condition. Preliminary studies on effect of various process parameters such as laser power, scanning velocity, and beam diameter on the performance parameters such as stress, strain, temperature distribution, bend angle and increment in bend angle are presented. The results showed that the bend angle per pass increases with the application of forced cooling. The efficiency and quality of laser bending process was found to be increased by applying forced cooling after each laser beam irradiation. These results will be useful to produce precise bend angle in difficult-to-form materials using lasers. Keywords: Precision bending, multi-pass laser bending process, forced cooling, finite element method, thermo-mechanical analysis

1.

INTRODUCTION REVIEW

AND

LITERATURE

Laser bending is an important process to bend the sheet metal worksheet by means of thermal stresses instead of external mechanical load. The thermal stresses are induced due to concentrated laser beam irradiation over the worksheet surface through a specified path [1]. It has many advantages over the conventional bending with tools and dies. The important features of laser bending process includes springback is not present, forming at inaccessible areas is possible, complex shapes can be generated with different irradiation strategies, possibility of bending brittle materials and the process can be easily controlled etc. [2-3]. The expensive hard tooling such as tools, dies, presses and additional loading arrangement is not required therefore the process is suitable for small scale production and fluctuating demand [4]. It has various applications like rapid prototyping, spatial forming, design shapes correction and welded

components alignment in naval, aerospace, medical and micro-electronics industries [5].

Fig. 1. Schematic of laser bending process In laser bending process, high energy laser beam irradiates over the worksheet surface as shown in figure 1. Temperature of the scanning

surface increases due to laser energy absorption. As the temperature increases, the heat flow occurs due to conduction, convection and radiation which results in the lowering down of irradiated surface temperature. Therefore, the process has two stages viz. heating stage and cooling stage. During heating, the irradiated surface is at higher temperature and thermal expansion occurs in the heated region. This expansion is constraint by the surrounding material which results in the induced compressive thermal stresses in the heated region. When these compressive thermal stresses exceed the temperature dependent yield (flow) stress, the plastic deformation occurs. Now during cooling, the heat flows in the surrounding material and therefore the surrounding material expands while due to cooling the irradiated surface contracts. As the irradiated surface is already undergone the plastic compressive deformation therefore, finally the worksheet bends in the direction of laser head as shown in figure 1. Li and Yao (2000) studied the effect of strain rate on laser bending process [1]. Zhang et al. (2002) studied the effect of various process parameters on laser bending process [2]. Shen et al. (2006) investigated the temperature distribution and deformation behavior of plates undergone two simultaneous laser beam scans [3]. Shen et al. (2009) investigated the laser bending process for the metal-ceramic bilayer materials [4]. Zhang and Xu (2004) investigated the effect of melting on laser bending process. They developed a numerical model capable of handling the effect of melting [5]. Birnbaum et al. (2007) investigated the effect of clamping over the laser bending process [6]. Shi et al. (2011) investigated the forming accuracy of various sheet geometries. They found that the sheet geometry significantly affect the bend quality and should be considered for accurate laser bending operations [7]. Literature reports significant research work on experimental and numerical analysis of single pass laser bending process. However, the bend angle per pass is small (mostly less than a degree). In many applications such as adjustment of assemblies and complex shape generation, it is insignificant to bend the sheet by such a small bend angle and it is needed to get higher bend angles. The possible solution is to use multiple laser beam irradiations or to use some mechanical force in conjunction with the laser beam irradiations. Scant literature is available on multipass laser bending and laser assisted bending process to get higher bend angle [8-9]. However, the multi-pass laser bending process has some limitations such as- a) the melting may occur as the worksheet is already heated during preceding irradiations, b) higher lead time due to idle time of worksheet cooling and c) less bend angle due to reduced temperature gradient. These limit the

applicability of multi-pass laser bending process in practice. One possible solution to this problem is to apply forced cooling with suitable coolant after each laser beam irradiation. The cooling can be applied by various methods such as cooling with moving jet, continuous cooling over entire bottom surface, cooling at both top and bottom surface, cooling between two constitutive laser scans etc. Also cooling can be categorized in terms of coolant used like air, water, oil, ice, liquid nitrogen cooling etc. Further it can be natural cooling and forced cooling. In the present work numerical analysis of laser bending with forced cooling by water at entire bottom surface has been carried out. Figure 1 shows the schematic of the arrangement used for numerical analysis. The comparative studies among the other variations of cooling methods and materials are out of scope of the present work. The accuracy and efficiency of multi-pass laser bending process depends on the selection of process parameters and cooling conditions in each laser beam irradiation. However there is very scant literature available on the multi-pass laser bending process with force cooling. Therefore, it is worth to investigate the multi-pass laser bending process with forced cooling. The present work is an attempt in this direction. In this work, numerical analysis of multi-pass laser bending process with forced cooling is carried out by using FEM. The efforts have been made to understand the mechanism of multi-pass laser bending process with forced cooling. The behavior of worksheet bending, temperature distribution and stress-strain distribution are studied. The preliminary results from FEM simulation are presented for magnesium alloy M1A sheet. Systematic experiments have been planned to validate the results predicted by the developed numerical model. 2.

DEVELOPMENT OF FINITE ELEMENT METHOD BASED NUMERICAL MODEL

Transient thermo-mechanical analysis of multipass laser bending of magnesium alloy M1A is carried out by using finite element method (FEM). The schematic of thermo-mechanical analysis is shown in figure 2. Initially the thermal analysis was carried out by employing various input process parameters such as worksheet geometry, material properties, laser power, scanning velocity, number of laser scanning passes and laser beam diameter. Based on the predicted temperature distribution during thermal analysis, various performance parameters viz. induced stresses and strains were computed in the mechanical analysis and further the bend angles were obtained.

distance of worksheet surface from lens focal point and is considered as equal to the stand-off distance (H),  is wavelength, 10.6 µm, f is lens focal length, 127 mm,

DL is laser beam diameter before

lens. 2.3 Thermal analysis The laser beam was irradiated over the worksheet surface and due to reflection the heat flux was absorbed partially by the worksheet. The transient temperature field generated due to laser beam irradiation was determined by using three dimensional heat conduction governing equation:

Fig. 2. Schematic of finite element model 2.1 Assumptions     

c

The worksheet material is isotropic and homogeneous. Melting of the worksheet does not occur during laser beam irradiations. The residual stresses are not present and the weight of worksheet is neglected. Von-Mises criterion is used for plastic yielding and Bauschinger’s effect is neglected in the simulation process. The energy dissipation due to plastic deformation is neglected.

T    k T  t

where

(3)

 is the worksheet density, c is the specific

heat, T is the temperature, t is the time, k is thermal conductivity. Thermal boundary was modeled by using natural convection and radiation heat loss. The convection heat loss ( qc ) was calculated by using:

qc  h Ts  Te 

(4)

where h  25 W m -K is the convective heat transfer coefficient for natural cooling and 2

2.2 Heat flux model The Gaussian distributed constant speed moving laser heat source was modeled and applied over the worksheet surface. Laser was assumed to be a heat source with continuous wave nature. The Gaussian distributed circular laser beam was applied at the upper surface of the worksheet. The distribution of laser heat flux was given by following equation:

 2r 2  2 P q(r )  exp  2   R2  R 

(1)

where,  is the absorption coefficient, P is the laser power, r is the distance from the center of the laser beam and R is the laser beam radius. The laser beam radius R was calculated from stand-off distance by using standard beam propagation equations as given below [10]:

  M 2 h 2   R  w0 1   2     w0   where w0  0.05 mm,

1

2

(2)

2M 2 f is laser beam waist and is  DL

M 2 is beam quality factor, h is the

h  5000 W m2 -K for the case of forced water cooling, Ts is the worksheet temperature and Te  20  C is the environmental temperature. The heat loss due to radiation ( qr ) was calculated by using:

qr   (Ts4  Te4 )

(5)

  5.67 10  8 W m2 -K 4 is StefanBoltzmann Constant, and   0.4 is the surface where

emissivity of the worksheet. 2.4 Mechanical analysis The temperature distribution from thermal analysis was given as input to the mechanical analysis. In laser bending process, the worksheet weight and residual stresses are negligible as compared to transient thermal stresses induced due to laser beam irradiation. The worksheet was assumed to be clamped at one side (shown in figure 1). Therefore, the mechanical constraint, zero displacement and zero rotation at one side (clamped side) of the worksheet was applied. It was assumed that the total strain and strain rate can be decomposed into elastic, plastic, creep and thermal components of strain and strain rate. However, the

deformation occurs at relatively short time scale and hence, the contribution of creep can be neglected. Therefore, the effect of creep was not considered. The total strain rate as a sum of elastic, plastic and thermal strain rate was given as below: (6)  total   elastic   plastic   thermal Elastic strains were calculated through an isotropic Hook’s law and yielding was determined by using Von-Mises criterion as below:

1 ( 1   2 )2  ( 2   3 )2  ( 1   3 )2    y2 2 where and

y

(7)

is the temperature dependent flow stress

1 ,  2 and  3

are x, y and z components of

stresses respectively. The strain rate dependent flow stress was given by:

 y  C m

(8)

where C is the strength coefficient and m is the strain rate sensitivity exponent. The C and m are temperature dependent parameters.

Full Newton ABAQUSTM. 3.

technique

in

a

FEM

solver

RESULTS AND DISCUSSION

Numerical simulations were carried out to study the multi-pass laser bending process using the developed model. The worksheet geometry of 60×40×2 mm3 was modeled and non-linear isotropic temperature dependent material properties of magnesium alloy M1A were employed from published data [11]. The forced cooling was applied after each laser beam irradiation to cool down the worksheet to the ambient temperature. The numerical results are as follows. In the present work, the laser beam irradiates over the worksheet surface and then the worksheet is allowed to cool with forced convection for 2 seconds. Figures 4-6 show the temperature history, stress history, and strain history of worksheet bending history at point A and B respectively for the process conditions of laser power (P) 300 W, scanning velocity (V) 1000 mm/min, stand-off distance 20 mm, and number of passes of about 12. Each laser beam irradiation is followed by 2 seconds of forced cooling.

Fig. 3. Meshed worksheet with stress distribution contours Fig. 4. Temperature history at point A and B 2.5 Meshing and solution methodology The worksheet continuum was discretized using three dimensional linear hexahedron eight node elements. The elements ‘C3D8T’ which are meant for the coupled thermo-mechanical analysis were used for the discretization. The heated and nearby region was discretized by using uniform mesh of element size 0.5 mm and outer region was discretized by using coarse biased mesh. The effect of mesh distortion on thermal analysis was not considered. In the thickness direction equidistance two elements were taken. The meshed worksheet after final bending with stress contours is shown in figure 3. The same mesh model was used for both thermal and mechanical analyses. The total numbers of nodes and elements were 5589 and 3520 respectively. The solution was done by using

Figure 4 shows the temperature history of multi-pass laser bending process at points A and B. The temperature of the worksheet increases as the laser beam irradiates over the worksheet surface. Due to forced convection (cooling), the sheet temperature reduces to room temperature which avoids the irradiated surface to reach the melting point even for successive multiple laser beam irradiations. It can also be observed that the peak temperature and temperature gradient at point A and B are nearly same for all laser beam irradiations. As the temperature increases, the thermal expansion occurs in the heated region. The expansion of the heated region is restricted by the surrounding material which is comparably at lower

temperature. Due to this restriction, the compressive stresses are induced in the heated region and tensile stresses in the surrounding material having less temperature comparatively. Thus compressive stresses are generated at top surface (point A) and tensile stresses are produced at bottom surface (point B). Figure 5 shows the x-direction thermal stress history at point A and B. The magnitude of stresses increases with the number of irradiations. It may be due to the fact that the thickness of the irradiated region increases with number of laser beam irradiations. Therefore, thicken sheet restrain more to the thermal expansion of the heated region. This leads to the higher thermal stresses generated in the heated region.

gradient between point A and B increases with the number of laser beam irradiations. It may be due to thickening of worksheet after each laser irradiation. Increase in thickness results in higher temperature gradient between top and bottom surface and higher bend angle. Due to plastic deformation in the heated region the worksheet bending occurs. Figure 7 shows the comparison of bend angles obtained during 12 laser beam irradiations with and without forced cooling. It is observed that the bend angle obtained with forced cooling is approximately double the angle obtained in the case of natural cooling. This may be due to the fact that forced cooling provides more and effective temperature gradients in comparison with those generate in the case of natural cooling.

Fig. 5. x-direction stress history Fig. 7. Total bend angle vs. number of laser beam irradiations (P = 300 W, H = 20 mm)

Fig. 6. x-direction plastic strain history The induced thermal stresses result in the thermal strain generation in the heated region. When thermal stresses exceed the temperature dependent flow stress, the plastic deformation occurs. Figure 6 shows the x-direction thermal strain history at point A and B. It can be observed that the plastic strains are compressive in nature at both points A and B. The worksheet bends due to plastic strain gradient between top and bottom surface (at point A and B). The plastic strain

Fig. 8. Increment in bend angle after each laser beam irradiations (P = 300 W, H = 20 mm) Figure 8 shows the variation in increment in bend angle after each laser beam irradiation. It can be noted that, during forced cooling, the increment in bend angle increases with each scan. However, in the case of natural cooling, the increment in bend angle per pass decreases with each scan. It may be due to fact that in natural cooling, the work sheet

temperature does not reduce to room temperature after each pass. This phenomenon preheats the worksheet for the next pass, which leads to less temperature gradient and higher peak temperature at the bottom surface. However in the case of forced cooling the worksheet temperature reduces to the surrounding temperature as shown in figure 4. This results in lower temperature at bottom surface and higher temperature gradient in the thickness direction. Therefore, the bend angle after each irradiation increases when forced cooling is applied. 4. CONCLUSIONS In present work, numerical simulations of multi-pass laser bending of magnesium alloy M1A with forced cooling is carried out by using finite element method. Three-dimensional nonlinear transient thermo-mechanical numerical model is developed to study the multi-pass laser bending process with forced cooling. The increment in bend angle per pass is found to be increased with each laser beam irradiations. The peak temperature in each laser pass is found to be almost same. The multi-pass laser bending with forced cooling was found to be very productive (about 100% more) in comparison with the natural cooled laser bending process. In the scope of present study, it can be concluded that, the forced cooling produces the required bend angle by employing approximately half of the number scans required in the case of natural cooling. Present work will further be extended in the direction of experimental studies and optimization of multi-pass laser bending of magnesium and its alloys. REFERENCES 1.

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2.

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4.

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