laser cutting of thick-section circular blanks: thermal stress prediction and microstructural...

ORIGINAL ARTICLE

Laser cutting of thick-section circular blanks: thermal stressprediction and microstructural analysis

Syed Sohail Akhtar

Received: 22 November 2012 /Accepted: 23 December 2013 /Published online: 12 January 2014# Springer-Verlag London 2014

Abstract Laser cutting of thick-section circular mild-steelblanks of 10 mm thickness is examined. Thermal and stressfields developed in the cutting zone are predicted using finiteelement method and the simulation conditions are selected inline with the experimental parameters. An experiment is car-ried out to assess the geometric features of the cut surfaces.The morphology of the cut sections are examined using opti-cal and scanning electron microscopes and energy dispersivespectroscopy is carried out for elemental composition of thecut surface. It is found that laser cutting of thick steel blanksresults in substantial conduction loss from the cutting zone,which results in high-temperature gradients and large stresslevels in the cutting section. The cut edge features such aslocal dross attachment, striation patterns, and microcrack for-mation in the cut section are also examined.

Keywords Laser . Residual stress . Microstructure . Finiteelement analysis . Thick section

1 Introduction

Cutting of sheet metals is one of the most important applica-tions of lasers in materials processing, and nowadays, it findswide applications in the industry. Laser cutting is a noncontactthermal process that involves fast processing and precision ofoperation. The most significant feature of laser cutting is itscapability to generate a highly concentrated volumetric heat

input to perform fast processing with high precision resultingin high-quality product and maximization of productivity.Increased process efficiency, quality, and flexibility help toreduce costs. The continuous effort in increasing output powerand improved beam quality of laser systems has extended thescope of industrial laser-cutting applications to cover theprocessing of larger thicknesses. However, the temperaturegradient in the cutting zone becomes significantly high whenthick sheet metal is cut, which, in turn, results in high stresslevels in the cutting section and, thereby, reduces the quality ofthe end product. If properly modeled, numerical techniqueprovides significant information on the mechanism of lasercutting and hence lowers the cost of experimentation.

Considerable research studies are carried out to examinethe laser-cutting process. Gross et al. [1] investigated the meltflow pattern inside narrow thick-section kerfs using numericalsimulation techniques and identified wave structures in themelt flow which reduced the drag and pressure forces avail-able for melt acceleration and subsequent expulsion. Theyreported that a higher assist gas pressure enhanced a morehomogeneous acceleration with less integration of the flowdown the kerf leading to less or delayed build up of melt.Sparkes et al. [2] reported that the major factor limiting the cutquality in inert gas laser cutting of 6- to 10-m-thick stainlesssteel plates using the high brightness fiber laser was thedifficulty in obtaining full melt ejection through the narrowcut kerfs. Yilbas and Akhtar [3] predicted residual stressformed around the laser cut edges of 1-mm-thin alloy steelsheet. They found that high stresses are formed in the region,where the temperature gradients are high, while temperature isless than the melting temperature of the substrate material.Theoretical and experimental studies on thick-section cuttingwith a laser beam were conducted by Kar et al. [4] where they

S. S. Akhtar (*)Mechanical Engineering Department, King Fahd University ofPetroleum and Minerals, Dhahran, Saudi Arabiae-mail: [email protected]

Int J Adv Manuf Technol (2014) 71:1345–1358DOI 10.1007/s00170-013-5594-5

considered the effects of various parameters including laserpower, spot size, and cutting speed. Moreover, they alsopresented a model for laser processing of thick-section metalswith the emphasis on potential applications of high speedthick stainless steel cutting. Duan et al. [5] reported that thegas flow field inside the laser cut kerf strongly depends on thegeometric shape of the cutting front that is determined by theinput laser cutting parameters such as laser power, cuttingspeed, and focus position. Increase in the inlet pressure, nozzleexit diameter, and overlap of the nozzle with the cut kerfimproved the gas flow field inside the kerf and enhancedefficient melt removal.

According to Mahrle et al. [6], the advantage of increasedcutting speed of fiber laser cutting of metal is mainly achievedin thin-section cutting (up to about 2 mm). However, theabsorptivity of the fiber laser radiation decreases with thesheet thickness (above 6 mm) unlike CO2 laser radiation; inwhich case, the absorptivity continuously grows with sheetthickness and the maximum absorptivity is attained withlarger sheet thicknesses. Ermoler et al. [7] introduced themathematical model for striation formation in laser cuttingof steel. They used nonlinear heat-conduction equation withvariable coefficients and introduced the mathematical methodfor smoothing the coefficients at the melting point. Inert gascutting of thick-section stainless steel and medium-thicknessaluminum using a high-power fiber laser gas examined byWandera et al. [8]. Their findings revealed that low surfaceroughness was achieved with the focal position inside theworkpiece, which was associated with the wider kerf forimproved melt ejection in thick-section metal cutting. Lasercutting process and thermal stress formation was carried outby Yilbas et al. [9]. They introduced the finite element methodto predict temperature and stress fields in the cutting section.

Although thermal stress development in the cutting sectionof the metallic materials, including steels, was investigatedpreviously [3, 10], the main focus of the research studies waslimited to thin sheet metal cutting for thickness of ≤5 mm.However, heat transfer taking place in the cutting regiondiffers significantly for the thick workpieces as compared withthin workpieces, such as 10 mm thickness as considered in thecurrent study. This, in turn, modifies the thermal stress statesin the cutting region and influences the end product quality.Therefore, in the present study, finite element model is devel-oped using ABAQUS code [10] to compute the thermal andstress fields during laser cutting of thick-section (thickness=10 mm) mild-steel circular blanks (diameter=15 mm). As thelaser thermal treatment involves the moving heat source andphase change in the irradiated region, a moving heat source isincorporated via user-subroutine DFLUX in ABAQUS codein line with experimental conditions. A laser cutting experi-ment is carried out to examine metallurgical and morpholog-ical changes, including the striation formation, microcrackdevelopment and dross attachment at the kerf surface.

2 Numerical simulation model

2.1 Finite element model

The finite element analysis is carried out using ABAQUS[11]. Figure 1 shows the schematic view of the laser cuttingof circular blank and the coordinate system. The incorporationof 3D analysis is required to accurately calculate the high-temperature gradients through the specimen thickness, arisingfrom the laser beam rapid heating and the subsequent rapidcooling. The accurate calculation of these temperature profilesis very important, because they dominate the local thermalexpansion and contraction of the laser-irradiated cut sections,which control the amount of plastic deformation and subse-quent thermal stress developed in the cut sheet. The FE meshis generated after the identification of the critical regions in thegeometry. The critical regions are considered those wherehighly increased temperature and strain fields occur duringlaser cutting, such as, the material volumes around the laserbeam path and the heat-affected zone. These regions areestimated experimentally from the cut samples which foundto extend in a zone of width equal to about five times the laserbeam diameter. A refined mesh is selected for the abovecritical regions in order to enable proper introduction of thelaser heat source, which is selected as Gaussian. This ensuredgood accuracy of predicted temperature and thermal stressvalues, as well as to made certain the convergence of thesolution at sensible computing times.

Sequentially coupled thermo-mechanical analysis is usedto describe the laser cutting analysis, which means that defor-mations depend on temperatures but temperatures are inde-pendent of deformation. Therefore, the thermal analysis is firstsolved to obtain the temperature field throughout the specimenas a function of time which is then provided as an input for thestress analysis, to determine the thermal stress fields in thelaser cut section. Continuum, three-dimensional six-node lin-ear heat transfer elements (DC3D6) are used in the thermalanalysis whereas for stress analysis, three-dimensional six-node linear stress elements (C3D6) are used. The mesh com-prises of 68,784 elements and 38,550 nodes.

2.2 Modeling of a moving heat source

The heat input to the workpiece fundamentally depends on thelaser beam energy supplied and the material surface absorp-tion capacity. In order to calculate the heat flux distribution atthe kerf surface, a laser beam source model is required. In thepresent analysis, the laser beam is assumed to introduce athree-dimensional Gaussian heat flux distribution as presentedin Fig. 1. The laser beam moves continuously with velocity Ualong the scanning path, which is along the circumference ofthe circular blank. The volumetric heat flux distribution iscomputed according to the formula:

1346 Int J Adv Manuf Technol (2014) 71:1345–1358

Q ¼ Imaxδe−δz 1−r f

� �e − x−rSinωtð Þ2þ y−rCosωtð Þ2

a2

� �ð1Þ

Imax is laser power peak density, δ is the absorption coeffi-cient, a is the Gaussian parameter, rf is the surface reflectivityand x, y, z are the axes. The laser beam scans the surface along

the circumference of the blank with r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2

p, i.e.,

circular laser blanking is carried out, and the laser beammotion follows the circumference of the laser cut blank witha constant angular velocity ω. In Eq. 1, constant angularvelocity “ω” is used with a value of 20 rad/s and accordingly,the resultant velocity is U=ω. rwhere “r” is the radius of theblank with a value of 7.5 mm. A user-subroutine DFLUX(coded in FORTRAN) is used to incorporate Eq. 1 for themoving volumetric heat sourceQ. It can be observed that xandycomponents of theU in circular trajectory are:Ux=rSinωtandUy=rCosωt. The effective penetration depth of the laser beamafter the keyhole formation is estimated through consideringthe multiple reflections from the cut edges and incorporatingthe exponential decay of incident laser intensity along theabsorption depth. It can be simplified as:

δ ¼ 1

Lln

Imax

IL

� �ð2Þ

where L is the thickness of the workpiece, Imax is the peakpower intensity at the workpiece surface, and IL is the laserpower intensity at the workpiece thickness. The laser beamaxis is parallel to the z-axis (Fig. 1).

The user-subroutine DFLUX in ABAQUS [10] is used tointroduce the volume flux described by Eq. (1). The subrou-tine first calculates the position of the laser beam according to

the cutting time, t, and then computes the heat flux, Q, at eachintegration point. The Gauss parameter “a” is taken as0.0003 m and velocity of 10 cm/s is used in accordance withthe experimental conditions.

2.3 Thermal analysis

In the laser heating analysis, the solid body heat conductionand phase change with temperature-dependent conductivity,internal energy (including latent heat effects), and convectionand radiation boundary conditions are considered. The Fourierheat transfer equation for the laser heating process can bewritten as:

ρDE

Dt¼ ∇ k∇Tð Þð Þ þ Q ð3Þ

where E is the energy gain of the substrate material, ρ is thematerial’s density, k is the thermal conductivity, and Q is theheat source term as defined in Eq. 1. In the case of a movingheat source along circumference of a circular blank with aconstant velocity U, energy gain of the substrate materialyields:

ρDE

Dt¼ ρ

∂E∂t

þ ρU∂E∂x

ð4Þ

or

ρDE

Dt¼ ρ

∂ CpT� �∂t

þ ρU∂ CpT� �∂x

ð5Þ

Combining Eqs. (3) and (5) yields

ρ∂ CpT� �∂t

¼ ∇ k∇Tð Þð Þ þ ρU∂ CpT� �∂x

þ Q ð6Þ

where Cp is the specific heat. To analyze the phase changeproblem, the enthalpy method is used [10]. The specific heat isassociated with the internal energy gain of the substrate ma-terial. However, the internal energy gain during the phasechange is associated with the latent heat of fusion, which isgiven separately in terms of solidus and liquidus temperatures(see Table 1) and the total internal energy associated with thephase change, called the latent heat. As the primary interest isthe stress field developed in the cutting section, the flow fieldgenerated in the liquid phase at the kerf surface during thelaser cutting process is omitted.

Fig. 1 Schematic view of laser cutting process and the coordinate system

Int J Adv Manuf Technol (2014) 71:1345–1358 1347

The convective and radiation boundary conditions are con-sidered at the free surface of the workpiece. Therefore, thecorresponding boundary conditions are:

At the irradiated surface:

∂T∂z

¼ hf

kTs−T ambð Þ þ εσ

kT 4s−T

4amb

� �

where hf=3,000 W/m2 K [12] is the forced convection heattransfer coefficient due to the assisting gas.

At the top and bottom surfaces:

∂T∂x

¼ h

kTs−T ambð Þ þ εσ

kT 4s−T

4amb

� �and

∂T∂y

¼ h

kTs−T ambð Þ

þ εσk

T4s−T

4amb

� �

where h=20 W m−2 K−1 is the heat transfer coefficient due tonatural convection, and Tsand Tamb are the surface and ambienttemperatures, respectively, ε is the emissivity (ε=0.9 is con-sidered), σ is the Stefan–Boltzmann constant (σ=5.67×10−8 W m−2 K−4). Initially (prior to laser cutting), and thesubstrate material is assumed to be at constant ambient tem-perature, i.e., T=Tamb, which is considered as constant (Tamb=300 K).

Equation (6) is solved numerically with the appropriateboundary conditions to predict the temperature field in thesubstrate material. Table 1 gives the properties of mild steelused in the simulations [13].

The thermal model consisted of two steps. The first step,which lasts 0.3141 s, simulates the response of the blank under

a moving laser heat flux along its circumference. The secondstep, which lasts for 300 s, simulated the continuous cooling inthe model. Cooling was allowed to continue until the blankreaches the initial temperature (room temperature). Thetemperature-time history resulting from the thermal analysisis used as input to the thermal stress analysis.

2.4 Stress analysis

Solidification involves small strain, so the assumption of smallstrain is adopted in this work. The thermal strains that domi-nate thermo-mechanical behavior during solidification are onthe order of only a few percent as confirmed by severalprevious solidification models [14]. The displacement spatialgradient is small ∇u=∂u/∂x so ∇u:∇u≈1 and the linearizedstrain tensor becomes [15]:

ε ¼ 1

2∇uþ ∇uð ÞTh i

ð7Þ

The small strain formulation can be used, where Cauchystress tensor is identified with the nominal stress tensor, and bis the body force density with respect to initial configuration.

∇⋅σ xð Þ þ b ¼ 0 ð8Þ

The rate representation of total strain in this elastic–viscoplastic model is given by ABAQUS [11]:

ε: ¼ ε:el þ ε:ie þ ε:th ð9Þ

where ε:el , ε

:ie and ε

:th are the elastic, inelastic (plastic+creep),

and thermal strain-rate tensors respectively. Stress rate σdepends on elastic strain rate, and in this case of linear

Table 1 Thermal and mechanical properties used in the simulations [13]

(a) Specific heat with temperature

T (K) 300 373 473 673 873 1,073 1,273 1,473

Cp (J kg−1 K−1) 500 520 530 580 680 670 640 620

(b) Thermal conductivity

T (K) 300 373 473 573 673 773 873 973 1,073 1,173 1,273 1,373

K (W m−1 K−1) 53 50 47 44 41 36 34 30 27 27 27 27

(c) Elastic modulus and Poisson’s ratio with temperature

T (K) 300 473 673 1,073 1,273 1,473 1,573 1,673

E (GPa) 200 185 175 125 100 75 55 30

υ 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32

(d) Thermal expansion coefficient with temperature

T (K) 300 473 673 873 1,073 1,273 1,473 1,673

α (1/K)×10−5 1.2 1.25 1.35 1.45 1.25 1.32 1.42 1.58

(e) Yield strength with temperature

T (K) 300 453 493 513 640 813 933 1,143 1,233 1,450 1,600 1,700

σy (MPa) 480 460 440 320 280 150 80 62 51 42 34 29

Density=7,860 kg/m3 ; latent heat of melting=247,000 kJ/kg; solidus temperature=1,758 K; liquidus temperature=1,788 K


isotropic material and negligible large rotations, it is given byEq. 10 in which “:” represents inner tensor product.

σ: ¼ D : ε:−ε:ie−ε:thð Þ ð10Þ

D is the forth order isotropic elasticity tensor given by 11.

D ¼ 2μIþ KB−2

3μ

� �I⊗ I ð11Þ

Here, μ, KB are the shear modulus and bulk modulusrespectively and are in general functions of temperature while

I and I are fourth- and second-order identity tensors and “⊗”is the notation for outer tensor product.

Inelastic strain includes both strain-rate-independent plas-ticity and time-dependant creep. Creep is significant at thehigh temperatures of the solidification processes and is indis-tinguishable from plastic strain [16]. The inelastic strain rate isdefined here with a unified formulation using a single internalvariable [17], equivalent inelastic strain εie to characterize themicrostructure. The equivalent inelastic strain rate ε ie is afunction of equivalent stress σ , temperature T, and equivalentinelastic strain εie .

ε:ie ¼ f σ; T ; εie

� �ð12Þ

σ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

3σ0ijσ

0ij

rð13Þ

σ0is a deviatoric stress tensor defined in 14.

σ0ij ¼ σij−

1

3σkkδij ð14Þ

The workpiece is assumed to harden isotropically, so theVonMises loading surface, associated plasticity and normalityhypothesis in the Prandtl–Reuss flow law is applied [18]:

ε:ieð Þij ¼

2

3ε:ieσ0ij

σð15Þ

In the stress analysis, displacements are stored at the nodalpositions as a solution variable, and loads are defined asprescribed displacements and forces. Employing the interpo-lation functions, it is possible to calculate the strain and stress

increments at any point within the element using the compat-ibility and constitutive equations. ABAQUS transforms themechanical equilibrium equations into a set of simultaneousequations, such that the nodal displacements and forces arerelated to each other through the elemental stiffness matrix.However, ABAQUS uses a temperature-dependent total ther-mal strain coefficient, ά(T). The differential and total thermalexpansion coefficients are related to each other through:

α0Tð Þ ¼ 1

T−To

Z T

Toα Tð ÞdT ð16Þ

where To is a reference temperature designating the point atwhich the material exhibits no dilatational strain (set to themechanical coherency temperature in the current problem)and α(T) is temperature dependant coefficient of thermalexpansion. InABAQUS/Standard analysis, a spatially varyingthermal expansion can be defined for homogeneous solidcontinuum elements by using a distribution, which includesthe tabulated values for the thermal expansion. ABAQUS usesan implicit backward-difference scheme for time integrationof both temperature and displacements at every material inte-gration point.

It should be noted that the thermal stress field is almost zero(hydrodynamic pressures are present only) in the moltensurface. The solid and liquid interface in the kerf vicinityremains at a solidus temperature, and the elastic modulereduces significantly at elevated temperatures, which is givenin Table 1. To account for the effects of material melting andre-solidification and annealing the ABAQUS command*ANNEAL TEMPERATURE was used. This commandcauses a point in the material to lose its hardening history bysetting the equivalent plastic strain at that point to zero if itexceeds a certain temperature. The annealing temperatureused was 1,788 K. To avoid computational difficulty, theyielding stress is limited to its value at the annealingtemperature.

3 Experimental details

ACO2 laser delivering nominal output power of 3 kWat pulsemode with different frequencies is used to irradiate the work-piece surface. The nominal focal length of the focusing lens is

Table 2 Laser cutting conditions used in the experiment

Cuttingspeed(cm/s)

Power(W)

Frequency(Hz)

Nozzlegap(mm)

Nozzlediameter(mm)

Focusdiameter(mm)

N2

pressure(kPa)

15 3,000 1,000 1.5 1.5 0.3 600


101.6 mm. The laser beam diameter focused at the workpiecesurface is 0.3 mm. Nitrogen assisting gas emerging from theconical nozzle and co-axially with the laser beam is used.

Mild-steel sheets with 10 mm thickness were used as work-piece. The laser cutting conditions are given in Table 2. Theprocess parameters are selected based on the quality of the endproduct (cutting section). Two parameters are found to beimportant: cutting speed and laser output power. In order toselect the process parameters, several tests are carried out. Inthis case, reducing the cutting speed by 15 % enhances thekerf width size and dross attachment; however, increasing thecutting speed by 15 % prevents the through cutting locally.However, increasing laser output power results in increasedkerf width size and dross attachment while reducing by 15 %locally prevents the through cutting. The morphologicalchanges at the kerf surfaces were examined using Jeol 6460electron microscope.

4 Results and discussion

Laser cutting of 15mmdiameter circular blank in 10mm thickmild-steel sheet is considered and temperature and stress fieldsin the cutting zone are modeled using the finite element codeABAQUS. The simulation conditions are selected accordingto the experimental conditions. The microstructural and

200

800

1400

2000

2600

3200

0 0.0118 0.0236 0.0354 0.0472

TE

MP

ER

AT

UR

E(K

)

DISTANCE ALONG THE TOP CIRCUMFERENCE (m)

t = 0.0785 s (Heat Source Location is at A)

t = 0.1570 s (Heat Source Location is at B)

t = 0.2356 s (Heat Source Location is at C)

t = 0.3141 s (Heat Source Location is at D i.e. End of Heating Cycle)

a

b

Fig. 3 a Temperature variationalong top circumference of theblank for different heatingperiods. b Temperature contoursat the kerf surface and inside theblank at the end of the heatingcycle (t=0.3141 s)

200

500

800

1100

1400

1700

0.00 0.05 0.10 0.15 0.20 0.25

TE

MP

ER

AT

UR

E (

K)

TIME (s)

Thermocouple is at 0.4 mm away from the cut edge

Predictions

Experiment

Fig. 2 Temporal variation of temperature predicted from the simulationsand obtained from thermocouple data at location at 0.4 mm away from thecut edge [10]


morphological changes in the laser cut region of the blank areexamined using various characterization techniques includingscanning electron and optical microscopes and EDS analysis.The geometric arrangement of the circular blank, coordinatesystem and various locations are identified in Fig. 1. As thecutting speed during laser cutting is kept 15 cm/s, the totaltime to cut the blank is 0.3141 s. As the cutting cycle iscomplete, the cut blank is allowed to cool to initial tempera-ture, which took 300 s.

To validate the model study, the simulation conditions areset in accordance with the previous work [10]. The predictionsof surface temperature variation and experimental data obtain-ed from the previous study are given in Fig. 2. It is evident thatpredictions of the model study agree well with the surfacetemperature data obtained from the previous study [10]. Thesmall discrepancies between both results are related to theexperimental errors and the assumption made in the modelstudy such as assumption of isotropic thermal properties.

4.1 Temperature and stress field predictions

Figure 3a shows the temperature variation along the topcircumference of the blank for the time periods corresponding

to the moments when laser beam is at locations A, B, C, andD, respectively, during the cutting cycle. Figure 3b showstemperature contours at the end of heating cycle (t=0.3141 s) when the laser beam is at location D. Temperatureattains its maximum at each location of the laser beam duringthe cutting process, which depicts that the laser beam changesits location around the blank circumference. It can be observedthat the temperature decays sharply from its peak value to theinitial temperature in the region corresponding to the edge ofthe laser-irradiated spot, which is due to the low workpiecetemperature in the neighborhood of the edge of the laser spot.However, temperature decays gradually behind the laser spotalong the circumference, which is attributed to the convectiveand conduction losses from the cutting section, which gradu-ally lower the temperature in this region. Moreover, the liquidphase heating across the irradiated spot results in temperaturedistribution similar to the laser power intensity distributionacross the melted spot, which is Gaussian. The maximumtemperature exceeds the melting temperature of the substratematerial resulting in the superheating of the liquid phase thattakes place in the cutting region at the laser-irradiated spotregions. In addition, phase change can also be observed fromthe temperature curves; in which case, the slow rise of

0.0E+00

1.2E+08

2.4E+08

3.6E+08

4.8E+08

6.0E+08

0 0.0118 0.0236 0.0354 0.0472

VO

N M

ISE

S S

TR

ES

S (

Pa)

DISTANCE ALONG THE TOP CIRCUMFERENCE (m)

t = 0.0785 s (Heat Source Location at A)

t = 0.1570 s (Heat Source Location at B)

t = 0.2356 s (Heat Source Location at C)

t = 0.3141 s (Heat Source Location at D i.e. End of Heating Cycle)

a

b

Fig. 4 aVon Mises stressvariation along top circumferenceof the blank for different heatingperiods. bVon Mises contours atthe kerf surface and inside theworkpiece at the end of theheating cycle (t=0.3141 s)


temperature occurs between solidus and liquidus tempera-tures. As the laser beam moves along the cut edges fromlocation A to D, temperature decay in the region behind thelaser spot becomes sharper. Such gradual decay of tempera-ture is attributed to the heat loss due to convection andconduction from the laser heated surface; i.e., initially heatedregion during the laser scanning cools gradually because ofheat loss from this region resulting in the formation of high-temperature gradients in this region.

Figure 4a shows the Von Mises stress variation along thetop circumference of the blank for the time periods when laserbeam is at locations A, B, C, and D, respectively, during thecutting cycle. Figure 4b shows Von Mises stress contours atthe end of heating cycle (t=0.3141 s) when the laser beam is atlocation D. Von Mises stress attains low values in the regionwhere temperature is high, which is associated with the lowelastic modulus of the workpiece at elevated temperatures(Table 2). However, the stress attains high values in the regionclose to the irradiated spot edge, particularly in the frontalregion of the laser-irradiated spot during the cutting process.This is attributed to large temperature gradient developed inthis region owing to the existence of significant temperaturedifference. Therefore, the elastic modulus remains high andthe high thermal strain due to the high-temperature gradient

results in high stress levels. The behavior of the stress acrossthe laser-irradiated spot as well as in the vicinity of the spotedge remains almost similar for all the heating periods. Themaximum thermal stress reaches almost 450 MPa along thecircumference at the top surface of the cutting section.

Figure 5a shows the temporal variation of temperature attwo locations A and C. Temperature attains high values whenthe laser heat source is located at points A and C. The rate oftemperature decay at both locations after the laser beammovesaway from these points is almost the same. In addition, the rateof temperature increase is higher than the decay rate of tem-perature at both locations, which is attributed to the largetemperature difference between the laser spot and the neigh-borhood of the laser spot, which are at initial temperature.Once the laser beam approaches these locations, temperatureincreases sharply. Moreover, once the laser beam passes overthese locations, conduction heating takes place because of thehigh-temperature gradient developed between the cuttingedge and its neighborhood. This reduces the time rate oftemperature decay at these locations. The decay rate of

200

700

1200

1700

2200

2700

0 0.2 0.4 0.6 0.8 1

TE

MP

ER

AT

UR

E (

K)

TIME (s)

Location A

Location C

0.0E+00

1.1E+08

2.2E+08

3.3E+08

4.4E+08

5.5E+08

0 0.3 0.6 0.9 1.2 1.5

VO

N M

ISE

S S

TR

ES

S (

Pa)

TIME (s)

Location A

Location C

a

b

Fig. 5 Temporal variation of temperature (a) and Von Mises stress (b) attwo locations: A and C

200

720

1240

1760

2280

2800

0 0.0118 0.0236 0.0354 0.0472

TE

MP

ER

AT

UR

E (

K)

DISTANCE ALONG THE CIRCUMFERENCE (m)

Bottom Circumference at z = 0.01 m t = 0.3141 s

t = 0.3641 s

t = 0.6641 s

t = 1.3141 s

t = 300.00 s

200

720

1240

1760

2280

2800

0 0.0118 0.0236 0.0354 0.0472

TE

MP

ER

AT

UR

E (

K)


Top Circumference at z = 0 m t = 0.3141 s

t = 0.3641 s

t = 0.6641 s

t = 1.3141 s

t = 300.00 s

A B C

DD

A B C

DD

a

b

Fig. 6 Temperature distribution along the top (a) and bottom(b) cut edgesduring different cooling periods after heating cycle ends at t=0.3141 s


temperature reduces significantly as the time progresses andreduces to initial temperature of 300 K. The correspondingtemporal variation of Von Mises stress at locations A and C isshown in Fig. 5b Von Mises stress rises rapidly for bothlocations (A and C) reaching its maximum just in front ofthe laser spot because of large temperature gradients in this

region. However, as time progresses, the stress reduces to alocal minimum and then increases with succeeding time. Thelocal minimum in stress is associated with the change in therate of temperature decay with the progressing time.Therefore, the temperature reduces abruptly from its peakvalue and as the time progresses, this decay rate becomes

1.00E+06

1.21E+08

2.41E+08

3.60E+08

4.80E+08

6.00E+08

0 0.0118 0.0236 0.0354 0.0472

VO

N M

ISE

S S

TR

ES

S (

Pa)


Top Circumference at z = 0 m t = 0.3141 s

t = 0.3641 s

t = 0.6641 s

t = 1.3141 s

t = 300.00 s

1.00E+06

1.21E+08

2.41E+08

3.60E+08

4.80E+08

6.00E+08

0 0.0118 0.0236 0.0354 0.0472

VO

N M

ISE

S S

TR

ES

S (

Pa)


Bottom Circumference at z = 0.01 m t = 0.3141 s

t = 0.3641 s

t = 0.6641 s

t = 1.3141 s

t = 300.00 s

A B C DD

A B C DD

a

b

Fig. 7 Von Mises stress distribution along the top (a) and bottom (b) cutedges during different cooling periods after heating cycle ends at t=0.3141 s

Fig. 8 Von Mises stress contoursat the kerf surface and inside theworkpiece at the end of thecooling cycle (t=300 s)

200

720

1240

1760

2280

2800

-0.0075 -0.005 -0.0025 0 0.0025 0.005 0.0075

TE

MP

ER

AT

UR

E (

K)

DISTANCE ALONG Y-AXIS AT THE MID-PLANE (m)

x = 0 m, z = 0.005 m (Along Line EF) t = 0.3141 s

t = 0.3641 s

t = 0.6641 s

t = 1.3141 s

t = 300.00 s

a

b

Fig. 9 a Temperature variation along the line EF (along y-axis) throughthe mid-plane for various cooling periods. bTemperature contours insidethe blank depicting line EF at the start of cooling cycle (t=0.3141 s)


steady. Consequently, change in temperature gradient fromsharp decay to gradual decay modifies the Von Mises stressin this region. Furthermore, temperature change also modifiesthe thermal expansion of the blank material, which, in turn,alters the thermal strain during the temperature change. Thisresults in the change of the stress state at this particularmoment. However, as time increases further, the cooling ofthe initially heated regions via conduction and convectioncauses the attainment of the steady residual stresses in theseregions. Therefore, the steady residual stress remains the sameafter further progressing of time.

Figure 6 shows temperature variation along the top andbottom circumferential edges of the cut blank for differentcooling periods. It should be noted that the cooling cyclestarts immediately after t=0.3141 s when the laser beam isswitched off and the cutting cycle ends. Temperature re-mains high at the initiation of the cooling cycle particularlyin the region where the laser cutting had terminated prior tocooling cycle. As cutting terminates at location D (whichcorresponds to 0.0471 m, the total distance traveled alongthe circumference), the adjoining location is the startinglocation of the cutting on the circumference, i.e., 0 m, whichalso corresponds to location D. As this location is alreadyheated previously at the start of cutting process, it undergoes

an annealing effect upon completion of the cutting processalong the circumference. Therefore, temperature gradient atlocation D becomes different than the other locations aroundthe circumference because of the annealing effect. As thecooling period progresses, temperature around the circum-ference reduces further. The rate of reduction is low atlocation D. As the cooling period increases further, temper-ature reduces to the initial temperature and cooling cycleends at t=300 s. In the case of bottom cut edge, similartemperature behavior can be observed as in the case of topedge. However, the peak temperature reduces slightly at thesurface of the cut edge because (1) the laser energy reachingthe bottom region of the cutting section is lower than that atthe surface and (2) the assisting gas cools the bottom edgeprior to exiting the kerf. Nevertheless, the reduction in thepeak temperature is not significantly high.

Figure 7 shows Von Mises stress variation along the topand bottom circumferential edges of the cut blank for differentcooling periods similar to the ones shown in Fig. 5 whereasFig. 8 shows Von Mises stress contours around the cut edgesat the end of cooling cycle, t=300 s. As can be seen, VonMises stress attains low values when temperature is higharound the cut edges, particularly in the irradiated region(location D) at the onset of cooling cycle, i.e., t=0.3141 s.

-4.00E+08

-3.00E+08

-2.00E+08

-1.00E+08

0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

-0.0075 -0.005 -0.0025 0 0.0025 0.005 0.0075

RE

SID

UA

L S

TR

ES

S (

Pa)

DISTANCE ALONG Y-AXIS AT THE MID-PLANE (m)

x=0 m, z = 0.005 m (Along Line EF)

t = 0.3141 s

t = 0.3641 s

t = 0.6641 s

t = 1.3141 s

t = 300.00 s

a

b

Fig. 10 aResidual stressvariation along the line EF (alongy-axis) through the mid-plane forvarious cooling periods. bResidual stress contours insidethe blank depicting line EF at theonset (t=0.3141 s) andtermination (t=300 s) of coolingcycle


This phenomenon is associated with temperature-dependentelastic modulus, which reduces with increasing temperature(Table 2). Consequently, thermal softening of the irradiatedregion results in the attainment of low stress in the high-temperature region. In addition, Von Mises stress attains highvalues in the region where the temperature gradient is high; inwhich case, the thermal strain increases with increasing tem-perature gradient. Therefore, the stress becomes high in theregion where temperature is low and the temperature gradientis high. This corresponds to the region next to the location=0 m around the top and bottom circumferences. However, asthe cooling period progresses, stress around the top and bot-tom circumferences reduce because of the free expansion andcontraction of the top and bottom surfaces. As the coolingperiod ends, temperature reduces to initial temperature and thestress field becomes the residual stress. Von Mises stressremains almost the same around the top and bottom circum-ferences and the magnitude of the stress is 380 MPa after thecooling cycle ends.

The variation of temperature across the mid-plane (alongthe line EF in Fig. 9b) is shown in Fig. 9a for different coolingperiods. The Fig. 8b shows the temperature contour plot at themid-plane cross-section at the onset of cooling when the laser

beam is just turned off at location E (t=0.3141 s). Sharptemperature decay from location E towards the inner regionof the blank (along the y-axis) can be observed at the onset ofcooling, particularly at the central region of the blank, which isstill at the initial temperature (300 K). This results in high-temperature gradient particularly in the kerf surface vicinitycorresponding to location E, which is attributed to thesuperheating of the liquid phase prior to the initiation of thecooling period. It can be noted that as the laser beam movesalong the blank circumference towards the end point E, tem-perature decay in the region behind the laser spot becomessharper due to convective and conduction losses resulting inlow-temperature values at location F (on the order of 700 K atthe onset of cooling). This leads to the formation of high-temperature gradients across the diameter of the blank.Nevertheless, when the cooling period progresses, a sharpdecay in the temperature can be observed, particularly nextto the kerf surface at location E. This is attributed to the abruptcooling of the superheated liquid in the irradiated region at theonset of cooling cycle. This leads to significant drop of tem-perature in this region resulting in slowing down of thecooling rate and hence reduction of the temperature gradientin the kerf surface at this location.

Striations

Top Edge

Bottom Edge

5 mm

Boundary Layer Separation (BLS)

Point

Fig. 11 Optical photographs oflaser cut kerf surface of the blank


Figure 10a shows the residual stress distribution across themid-plane along the line EF for different cooling periodssimilar to those shown in Fig. 9a. Figure 10b shows the stresscontour plot at the mid-plane cross-section of the laser cutblank at the onset and termination of cooling cycle, respec-tively. It should be noted that at the end of the cooling cycle,temperature reduces to initial temperature and the stress fieldbecomes residual stress in the substrate material. It is evidentthat the residual stress is compressive in the neighborhood ofkerf surface regions E and F and becomes tensile towards thecenter of the blank. The peak value of this compressiveresidual stress lies at a location some distance away from thekerf surfaces on both sides. The attainment of the peak resid-ual stresses at locations close to the kerf surfaces is due to thehigh-temperature gradients formed in these regions, which ismore pronounced at location E as compared with F. In addi-tion, high thermal strain formed is compressive because ofthermal compression taking place in these regions. This con-tributes significantly to the attainment of the high thermallyinduced residual compressive stress in these regions. Themaximum residual stress is on the order of −260 MPa, whichoccurs at the kerf vicinity. The findings related to the residual

stress provide information on the stress levels. Consequently,the maximum stress level can be considered as limiting caseand can be reduced to minimize the influence of the thermalstresses on the cut edges with the help of proper setting of thecutting parameters.

4.2 Morphological and microstructural analysis

The main features on the thick-section steel laser cut edge thatsignify the efficiency of melt removal from the cut kerfinclude the striation formation, boundary layer separationpoint on the kerf surface and dross attachment on the bottomcut edge of the blank. The dynamical behavior of the lasercutting process affects the shape of the cutting front and themelt flow mechanism resulting in the formation of striationson the cut edge which are clearly visible in the optical photo-graphs (Fig. 11) and scanning electron micrographs (Fig. 12).The profile of the cut edges shown in Fig. 11 depicts theappearance of boundary layer separation point on the cut edgewhere the flow separates from the kerf wall and the melt flowregime transitions from a laminar boundary layer flow to aturbulent boundary layer flow. As depicted in Fig. 11, the

Kerf Surface

Striations

Top Region

Mid Region

Bottom Region

Micro-cracks

Re-solidified layer

Dross Attachment

Fig. 12 SEM micrographs of thekerf surface


striation pattern above the boundary layer separation pointfollow straight contours along the cut thickness at about onehalf of the total depth, but its pattern below the separation lineis irregular with slanting contours. This flow separation phe-nomenon at the kerf wall is attributed to the increase in viscousshear in the boundary layer, which retards the melt streamlinesand thickens the melt layer to satisfy continuity within thelayer. The possible cause of the increase in the viscosity of themelt is the oxidation reaction at the kerf surface during thecutting process, in which case the oxygen diffusion occursinto the melt. It is also reported [19] that the viscosity ofmolten metal with high oxygen content increases with tem-perature. It should also be noted that the viscosity of themolten flow further reduces because of reduction in tempera-ture at the exiting edge of the kerf surface. Another reason isalso attributed to the momentum of the assisting nitrogen gas,which reduces towards the kerf exit and hence results inreduced drag force in this region. The energy dispersivespectroscopy (EDS) is used to examine the level of oxidationof the melt by analyzing the elemental composition of the kerfsurface. The EDS results (shown in Fig. 13) confirm theexistence of high oxygen content at the kerf surface. It isnotable that the oxygen content is more at the mid region ascompared with the top section resulting in more viscous melttowards the exiting edge of the kerf. It also shows that thenitrogen gas pressure in the kerf is not sufficient to prevent thehigh-temperature oxidation reactions in the cutting section.

The close examination of the surface via SEMmicrographs(Fig. 12) reveals that microcracks are formed at the kerf of thelaser cut blank, which can be attributed to the rapid solidifi-cation of the melt. This is because of the high cooling rates,which results in high thermal stress field in this region.

However, no specific crack pattern is observed and crackpropagates almost in all directions at the surface. This indi-cates that the cooling is multidirectional and temperaturegradient in the region is considerably high as also observedin numerical predictions. Therefore, the thermal expansionand consequent contraction of the surface results in crackformation in the molten layer. Moreover, the contribution ofoxygen diffusion in the molten zone also contributes to thefine cracking at the surface onset of the rapid solidification.

As shown in Fig. 12, some melt buildup at the bottomregion of the cutting surface can be observed which is associ-ated with the thickening of the molten layer. In this case, thethickening of the solidified melt increases against the assistinggas drag force and the surface tension tends to round themolten buildup in this region. Hence, the molten flow withhigh values of surface tension and viscosity are more difficultto eject from the cut kerf by the assist gas jet and result inadherent dross on the lower cut edge as depicted in Fig. 12.

Re-cast Layer

Heat-A ected Zone (HAZ)

ff

Fig. 14 SEM micrograph of cutting edge cross-section depicting theheat-affected zone

Spectrum C O Mn Fe Total

Spectrum 1 1.40 32.53 1.00 65.07 100.00

Spectrum 2

Spectrum 3

Spectrum 4

Spectrum 5

Spectrum 6

Spectrum 7

0.00 0.00 2.16 97.84 100.00

1.54 0.00 1.37 97.09 100.00

1.84 18.71 0.92 78.53 100.00

2.48 31.32 0.86 65.33 100.00

2.05 3.02 1.52 93.42 100.00

1.73 34.60 0.81 62.86 100.00

Spectrum C O Mn Fe Total

Spectrum 1 5.33 37.39 0.82 56.47 100.00

Spectrum 2 5.33 32.90 0.00 61.77 100.00

Spectrum 3 4.60 33.79 0.00 61.62 100.00

Spectrum 4 7.94 35.06 0.78 56.23 100.00

Spectrum 5 6.05 34.77 0.00 59.18 100.00

Spectrum 6 5.29 36.53 0.91 57.27 100.00

a

b

Fig. 13 EDS analysis of the kerfsurface taken a near the top edgeand b at the mid-region


The cross-sectional examination of the cut sections also con-ducted to investigate the heat-affected zone (HAZ). The SEMmicrograph shown in Fig. 14 reveals that the heat-affectedzone is considerably narrow because of the localized heatingand contribution of convection and conduction heat transfer tothe cooling rates from the cut edges. Moreover, the assistinggas flow also restricts the width of the HAZ.

5 Conclusions

Laser cutting of mild-steel circular blanks of 10 mm thicknessis examined and temperature as well as thermal stress fieldsare predicted using the finite element code ABAQUS in linewith experimental conditions. Optical and scanning electronmicroscopes, and electron dispersive spectroscopy techniquesare used to examine the morphological and microstructuralchanges in the laser-cut region. It is found that the maximumtemperature along the cut edges exceeds the melting temper-ature and superheating of the liquid phase in the laser-irradiated region occurred. The temporal variation of temper-ature reveals that the temperature rise is rapid at the location ofthe laser beam location. As the laser beam moves away fromthese locations, the temperature decay becomes rapid. VonMises stress attains high values in the vicinity of the cuttingedges during the cutting process. However, considering thechange in temperature gradient along the cutting direction,thermal strain developed in the cutting zone is modified,which, in turn, reduces VonMises stress to its local minimum.As the cutting progresses, the initially heated sections alongthe cut edges cool down to low temperature and the stressfields become the residual stresses. The residual stress remainshigh along the cut edges. A boundary layer separation point onthe kerf surface was found, which clearly signify the striationpattern profiles on the kerf surface. The striation pattern abovethe boundary layer separation point follows straight contoursalong the cut thickness, but its pattern below the separationline is irregular with slanting contours, which is attributed tothe increase in viscous shear in the boundary layer, whichretards the melt streamlines and thickens the melt layer. Themajor cause of the increase in the viscosity of the melt wasfound the oxidation reaction at the kerf surface during thecutting process as revealed from energy dispersive spectros-copy analysis of the kerf surface. The thickening of the moltenlayer towards the kerf exit resulted in somemelt buildup at thebottom region of the cutting surface. Scanning electron mi-crographs revealed multidirectional microcracks at the kerfwhich can be attributed to the rapid solidification of the meltbecause of extremely high cooling rate resulting in highthermal strain due to thermal expansion and consequent con-traction of the kerf surface. The oxygen diffusion in the moltenzone as a result of oxidation reactions also contributes to finesurface cracking at the onset of rapid solidification.

Acknowledgments The author would like to acknowledge the supportof King Fahd University of Petroleum and Minerals, Dhahran, SaudiArabia. The author is also indebted to Distinguished Professor B. S.Yilbas for his continued support and helpful suggestions for conductingthis work.

References

1. Gross M, Celotto S, O’Neill W (2006) Melt flow in narrow thicksection kerfs. In: ICALEO 2006 Congress Proceedings, Scottsdale,Arizona (Laser Institute of America, Orlando). Paper 403, pp. 206–210

2. Sparkes M, Gross M, Celotto S, Zhang T, O’Neill W (2008) Practicaland theoretical investigations into inert gas cutting of 304 stainlesssteel using a high brightness fiber laser. J Laser Appl 20:59–67

3. Yilbas BS, Akhtar SS (2011) Laser cutting of alloy steel: three-dimensional modeling of temperature and stress fields. MaterManuf Process 26:104–112

4. Kar A, Scott JE, Latham WP (1996) Theoretical and experimentalstudies of thick-section cutting with a chemical oxygen-iodine laser(COIL). J Laser Appl 8:125–133

5. Duan J, Man HC, Yue TM (2000) Simulation of high pressure gasflow field inside a laser cut kerf. In: Proceedings of ICALEO 2000Section B (Laser Institute of America, Orlando), pp 87–96

6. Mahrle A, Lütke M, Beyer E (2010) Fibre laser cutting: beamabsorption characteristics and gas-free remote cutting. Proc IME CJ Mech Eng Sci 224:1007–1018

7. Ermolaev GV, Kovalev OB, Orishich AM, Fomin VM (2006)Mathematical modelling of striation formation in oxygen laser cut-ting of mild steel. J Phys D Appl Phys 39:4236–4244

8. Wandera C, Salminen A, Kujanpaa V (2009) Source Inert gas cuttingof thick-section stainless steel and medium-section aluminum using ahigh power fiber laser. J Laser Appl 21(3):154–161

9. Yilbas BS, Arif AFM, Abdul Aleem BJ (2009) Laser cutting of holesin thick metals: development of stress field. Opt Lasers Eng 47(9):909–916

10. Yilbas BS, Akhtar SS, Karatas C (2012) Laser hole cutting into Ti–6Al–4V alloy and thermal stress analysis. Int J Adv Manuf Technol59:997–1008

11. ABAQUS (2009) Theory Manual Version 6.7. ABAQUS Inc,Pawtucket

12. Shuja SZ, Yilbas BS (2000) The influence of gas jet velocity in laserheating—a moving workpiece case. Proc Inst Mech Eng C J MechEng Sci 214:1059–1078

13. Chen J, Young B, Uy B (2006) Behaviour of high strength structuralsteel at elevated temperatures. J Struct Eng 132(12):1948–1954

14. Risso JM, Huespe AE, Cardona A (2006) Thermal stress evaluationin the steel continuous casting process. Int J Numer Methods Eng65(9):1355–1377

15. Mase G, Mase GY (1999) Continuum mechanics for engineers, 2ndedn. CRC Press, Boca Raton

16. Li C, Thomas BG (2004) Thermo-mechanical finite-element modelof shell behavior in continuous casting of steel. Metal Mater Trans B35B(6):1151–1172

17. Anand L (1989) Constitutive equations for the rate dependant defor-mation of metals at elevated temperatures. ASME J Eng MaterTechnol 104:12–17

18. Mendelson A (1983) Plasticity: theory and applications. Krieger Pub.Co, Melbourne

19. Yilbas BS, Nickel J, Coban A (1997) Effect of oxygen in laser cuttingprocess. Mater Manuf Process 12:1163–1175


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