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2009 International Automotive Body Congress (IABC) November 4-5, 2009, Troy, Michigan, USA

Control of Springback in Bending and Flanging Advanced High Strength Steels (AHSS)

Hyunok Kim1, Menachem Kimchi1 and Taylan Altan2

1Edision Welding Institute (EWI), Columbus, OH 43221-3585

hkim@ewi.org; mkimchi@ewi.org

2Center for Precision Forming (CPF), The Ohio State University, Columbus, OH 43210-1271 altan.1@osu.edu

ABSTRACT In this study, springback for bending and flanging advanced high-strength steel (AHSS) was investigated by using experimental

methods and computation models. The elastic and plastic properties of AHSS were determined by using the tensile test and the biaxial

bulge test. Dual-phase (DP) 600 showed significant decreases about 10% of unloading elastic modulus as the effective strain

increased during loading and unloading cyclic tensile tests, while aluminum-killed drawing quality (AKDQ) gave almost constant

modulus. Therefore, a general expectation of constant elastic modulus of material will not always apply to AHSS. The V-bend test

was used to investigate the effects of material properties, texture orientations, and die openings on springback. The experimenatal

results showed that TRIP 780 has relatively smaller springback compared to DP 780 and 780 HY (high yield) materials at two

different die opening lengths. Experimental results were compared to the predictions of computation model. Preliminary tests with an

S-rail flanging die were conducted with AKDQ material to investigate the feasibility of this test method for springback study. In

addition, finite-element (FE) simulations for S-rail flanging of AKDQ and DP 780 were conducted to predict the thinning distribution.

Springback simulations were conducted for DP980 S-rail part with constant and variable elastic modulus. The variable elastic modulus

gave the higher magnitude of springback compared to the constant elastic modulus model.

Keywords: springback; bending; stamping; finite element method (FEM); advanced high strength steels (AHSS)

1.0 INTRODUCTION

Advanced high-strength steels (AHSS) have been increasingly used for automotive structural components, allowing improvement in

the crashworthiness without corresponding weight increases. Forming AHSS causes more severe springback compared to other

conventional mild steels and high-strength low alloy (HSLA). It requires much harder dies that are more expensive to rework for

compensating springback. AHSS is known to have unique elastic and plastic material behaviors. This becomes more difficult for

press-shop engineers and forming tool designers to control or compensate for springback in their production and tooling design.

Therefore, it is desirable to develop a reliable methodology to evaluate the effects of material properties (i.e., elastic-modulus,

hardening models, and anisotropy) on springback. The objective of study is to predict and reduce springback in bending and flanging

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AHSS. Example parts formed by bending and flanging can be side-rails and cross-members that are usually made with higher grades

of AHSS materials.

2.0 BACKGROUND

Springback behavior of sheet materials has been studied for many years [1, 2, 3, 4, 5, 6, 7, 8, 9]. This issue became more important

with the advent of AHSS. The magnitude of springback correlates with elastic modulus and the hardening behavior of sheet material.

There are a number of literatures on modeling of springback in forming AHSS. Important references are briefly summarized here in

several aspects; the effects of i) variable elastic modulus, ii) plastic material properties (i.e. kinematic hardening, Bauschinger effect,

anisotropy) on springback, and iii) compensation methods for springback in forming AHSS.

The change of elastic modulus with increasing plastic strain was investigated first by Lems [10] and then more recently by Morestin

using a uni-axial tensile test during loading process [11]. In a microscopic view, elastic modulus can be dependent on alloying

elements, the grain size and pile-up of dislocations near to grain boundary [12, 13, 14, 15]. Cleveland and Ghosh found that the slope

of the elastic modulus variation was different during loading and unloading, and explained that the difference was due to micro-plastic

strain, which did not overcome the barriers set up during forward flow nor created storage of a new dislocation network [16]. Thibaud

determined the elastic modulus variation of low-alloyed TRIP steels with plastic deformation by using vibrometric identification

method which uses beam and plate vibration theories [17] and Kwon showed the variation of elastic modulus using the indentation test

[18]. Zhu et al. 2004 found that the change in elastic modulus decreased from 6 to 12 % for mild steels and from 9 to 25% for AHSS

when the strain increased from 1 to 5% [19]. On the other hand, Perez found that elastic modulus was not changed with pre-strain

during loading process [20]. Therefore, the investigation of elastic modulus variation during loading and unloading, and the

development of an evolution model that can explain this behavior adequately would improve the accuracy of springback prediction in

FEM.

In sheet metal forming, the thorough understanding of the hardening models which describe the proper material behavior is very

important for accurate springback prediction. [21, 22, 23]. The mathematical theory of elastoplasticity is now well understood since

several works of Hill, Chaboche et al and Khan et al [24, 25, 26]. Isotropic hardening model may not be so effective when the material

undergoes non-monotonous deformations [27, 28]. To reproduce this Bauschinger effect, Prager and Ziegler proposed the linear

kinematic hardening model, resulting in underestimating the springback because this model considers the yield surface without

changing its shape and size [29, 30]. Besides the Bauschinger effect, several models were proposed to explain the transient behavior

during reverse loading [26, 31, 32]. Among these models, the Chaboche model has gained some popularity. [25, 33]. Chun further

improved the cyclic hardening model of Chaboche, and proposed modified versions of Chaboche models by considering the kinematic

hardening parameters as functions of the effective plastic strain. This combined hardening model of isotropic-kinematic law is

considered suitable in predicting the springback [27, 28, 34, 35]. Recently, Choi et al proposed rotational hardening model which

describes the multi-axial elastoplastic behavior [36, 37]. Besides these phenomenological models, there are also several models to

explain the material behavior from microstructural point of view [38, 39, 40, 41].

General guidelines for form dies and part design were developed to minimize and compensate springback in forming AHSS [42].

Using the flexibility of speed and position control in servo-motor driven press, the effect of forming speed, dwelling time at bottom

dead center and the sheet thickness on springback was investigated with ultra-high-strength steel and no effect of forming speed and

dwell time on springback on springback was found [43]. Warm forming was attempted to reduce springback in forming a U-channel

with DP980, DP780, DP590 and DP440 and mild steels [44]. Zero springback was observed at forming temperature of 800°C and a

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significant reduction of springback was found in forming at 400°C. Similar results were also found in the warm forming studies using

V-bend and U channel bend tests with AHSS [45]. Electormanetic forming method was introduced to reduce springback in the L-

shaped part bent with DP600 and TRIP700 [46]. Although, warm forming and electromagnetic forming demonstrated their novel

capabilities to reduce springback in bending and flanging AHSS, they are not very practical methods currently to apply to stamping

production, thus more development works need to be done.

Springabck of automotive stamping designs were studied with various AHSS [47, 48]. Springabck of a fender load beam stamped with

DP600, DP780 and DP980 and mild steel were compared and the maximum springback was observed in the highest strength material,

DP980 [47]. FE predictions of springabck were compared with several cross-section profiles of DP980 fender load beam [48]. These

studies of springback with actual parts concludes that a better model representing the unique forming characteristics of AHSS such as

the change of unloading elastic modulus with increasing plastic stain, Bauschinger effect and kinematic hardening needs to be

adequately modeled in FE simulations for accurate springback predictions. Therefore, a fundamental understanding of springback,

including the determination of the effects of elastic modulus and hardening behavior, is necessary to improve the status of forming

technology for AHSS.

3.0 APPROACH

In this study, two test methods, a simple V-bend test and the S-rail flanging test, were used to evaluate springback in bending and

flanging. The material properties of various grades of AHSS (DP 600, DP 780, and TRIP 780) were characterized by using tensile

tests and the viscous pressure bulge (VPB). In addition, from the cyclic loading-unloading tensile test, the change of elastic modulus

for increasing plastic strain was measured during loading and unloading. With these material input data, finite-element (FE)

simulations for selected tests were conducted to understand springback predicted at each test conditions and determine critical

experimental conditions/tool geometry that can allow to reliably measure springback. Experiments results of the V-bend test and the

S-rail flanging test were compared to FE predictions.

3.1 Characterization of Material Properties

In this task, tensile specimens (ASTM E646-98) were prepared along the rolling direction by using the wire electric discharge machine

(EDM). Three different materials [dual-phase (DP) 600, aluminum-killed drawing quality (AKDQ), and 304 stainless steel] were

tested with the Instron machine at The Ohio State University (OSU).

The goal of the test was to investigate the change of elastic modulus during the cyclic loading-unloading tensile test. In sheet metal

forming, elastic modulus is one of the key parameters for determining springback. A constant elastic modulus normally is used in

springback predictions with finite-element analysis (FEA) and mathematical methods. However, there are several results in the

literature presenting the change of elastic modulus during loading and unloading as the plastic strain increases. Therefore, with the

standard tensile test (ASTM E646-98), the cyclic loading and unloading was conducted at various strain levels to obtain loading and

unloading modulus as a function of strain. DP 600, AKDQ, and 304 stainless steel specimens were loaded and unloaded to particular

strains of 4, 8, 12, and 15% to obtain the loading and unloading modulus as a function of strain.

Figure 1 shows the true stress-strain curves measured with both a mechanical extensometer and a laser extensometer during the cyclic

loading and unloading test. In the test, the maximum difference of measured strains was 0.001 between the mechanical extensometer

and laser extensometer. However, because the mechanical extensometer showed more continuous data compared to laser

extensometer, the strain measurements from mechanical extensometer were used in calculations of loading and unloading modulus. In

flow stress, nonlinear zones were observed when loading curve changed to unloading curve due to hysteresis in the material. These

zones were not considered in calculating the elastic modulus. Similar tests were conducted for AKDQ and 304 stainless steel. The

loading and unloading modulus were obtained by fitting the stress-strain data in the loading or unloading part of stress strain curve to a

straight line.

Figure 1: Flow Stress Diagram for DP 600 Material Measured in the Cyclic Loading and Unloading Tensile Test as a Function of

Strain

The elastic loading modulus and unloading modulus were calculated from the cyclic loading/unloading tensile test. Figure 2 shows

about 10% decrease of elastic modulus for DP 600 as the plastic stain increased from zero to 0.14. The loading modulus and

unloading modulus decreased from 200 to 180 GPa at strain of 0.04 and remains constant in the range of 180 to 170 GPa up to the

strain of 0.14.

Figure 2: Variation of Loading Modulus and Unloading Modulus with Strain for DP 600 Material in the Cyclic Tensile Test

Similarly, the variations of elastic modulus for AKDQ and 304 stainless steel materials were plotted in Figures 3 and 4, respectively.

AKDQ showed small difference between loading and unloading modulus. However, as shown in Figure 4, 304 stainless steel gave

20% decrease of elastic modulus from 200 to 165 GPa at plastic strain of 0.4. This large change of elastic modulus is known to be

caused by so-called “TRIP EFFECT” which is the retained austenite transforms to martensie due to straining hardening.

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Figure 3: Variation of Loading Modulus and Unloading Modulus with Strain for the AKDQ Material in the Cyclic Tensile Test

Figure 4: Variation of Loading Modulus and Unloading Modulus with Strain for the 304 Stainless Steel Material in the Cyclic Tensile Test

These results indicate that the elastic modulus of AHSS and stainless steel should be considered as a function of plastic strain. The

elastic and plastic material properties of AHSS were determined by the standard tensile test (ASTM-E8) and detailed properties of

AHSS are given in Table 1 and these properties were used later as the input data for FE simulations.

Table 1: Material Properties of AHSS

R-Values

(Anisotropy) Material Thickness (mm)

E (GPa)

Y (MPa)

UTS (MPa)

U.E. (%)

T.E. (%) R0 R45 R90

DP 780 1.0 196 360 867 9.0 17.5 0.802 0.90 0.874 DP 780 HY 1.0 201 391 838 7.7 17.5 0.843 1.108 0.931 TRIP 780 1.0 193 378 819 14.5 19.5 0.498 0.872 0.583

The larger range of plastic data for AHSS was determined by the VPB test, because the tensile test gave relatively smaller rage of

data. While the tensile test provides the maximum strain of 0.15 for AHSS, the bulge test can provide the larger strain data up to 0.4

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that is often observed in stamping. Figure 5 illustrates the VPB test. The initial setup of test is shown in Figure 5(a). A 10- × 10-in.

square samples is clamped with the lock bead of the die to prevent any metal flow into the bulged dome during the test. The upper

ram moves down and the sheet is bulged with a viscous media that is pressurized with a stationary punch. The final shape of sample

and the schematic of test device are shown in Figure 5 (b). During the test, two parameters such as dome height and the pressure are

measured with the data-acquisition system. The measured data were used to calculate the true stress-strain curve for the tested sheet

materials as shown in Figure 6.

(a) Before the test (b) After the test

Figure 5: Schematic of VPB Test

Figure 6: Flow Stress Data Determined by the VPB Test

3.2 Evaluation of Springback by using the V-Bend Test

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The V-bend test was used to investigate the effects of material properties, sheet orientation, and die opening length on springback.

The V-bend tooling was installed in the Instron machine. Figure 7 gives the picture of test setup and the schematic of the bending

configuration. Detailed dimensions of the sample and the bending tools are given in Table 2.

Figure 7: The V-Bend Test used for Springback Test

Table 2: Dimensions of Sample and Bending Punch/Die

Parameters Descriptions Sample size 40-mm wide × 90-mm long × 1 ~1.6-mm thick Punch radius 0.2 mm Die radius 20 mm Die opening Two times and eight times of sheet thickness Punch speed 0.5 mm/s

From preliminary FE analyses of V-bending, the larger die opening length (w) was predicted to increase springback angle after V-

bending. Thus, in this study, two different die opening lengths that were equal to two times and eight times of initial sheet thickness

were used in experiments. Three different AHSS materials of the same thickness (1 mm) were tested as shown in Table 3. Two

different orientations relative to the rolling direction (RD) and transverse direction (TD) of sheet sample were used. The RD samples

had the bending line parallel to the RD of the sheet, which is known to have less bendability compared to bending sheet in TD. Three

samples were tested at each test condition.

Table 3: Test Matrix for V-Bend Test

Die Opening (2t) Die Opening (8t) Materials Thickness (mm) RD TD RD TD

DP 780 3 3 3 3 DP 780 HY 3 3 3 3 TRIP 780

1 3 3 3 3

The following steps were taken for the springback tests:

• The die opening was fixed to be two or eight times the initial sheet thickness.

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• The first specimen was bent until it failed.

• From the load-stroke curve measured for the first sample, the 90% of maximum load was used as a limit for bending of each

material to avoid necking for the springback test (see Figure 8).

• The bending angles of the sample were measured before and after withdrawing the punch.

Springback angle was determined by measuring the bending angles of sample before and after withdrawing the punch. Different

AHSS materials were tested at different angles, because of different maximum punch forces and their 90% stroke limits of three

materials. A dimensionless springback parameter, relative springback (= springback angle/bend angle), was used to compare the

springback for different AHSS. However, for the bend test with w = 8t, the same bending angle (i.e., same punch stroke) was used

selectively for DP 780 HY (high yield) (RD/TD) and TRIP 780 (RD/TD) to compare the springback angle at same bending angle.

Figure 8: Load-Displacement Curves for Determining the Bending Limit for Springback

A quarter FE model with symmetric boundary conditions was prepared for V-bending to reduce the computation time, as shown in

Figure 9. The five brick elements were used in thickness direction.

Figure 9: FE Model for the V-Bend Test 8

The forming simulation was conducted first by moving down the punch and the springback simulation was subsequently conducted by

withdrawing the punch from the end of forming stage. Figure 10 compares the punch force-stroke curves between FEM prediction

and experiments of DP 780 HY with RD and TD. In FE simulations, constant elastic modulus determined by tensile test was used for

each material and the biaxial bulge test data was used for the plastic material properties.

Figure 10: Comparison of Load-Stroke Curves between Experiments and FE Prediction

From FE simulations, the stress and strain on the cross section of sheet were plotted for DP 780 HY in Figure 11. As expected, the

inner bending zone is under compression, while the outer bending zone is in tension. The maximum plastic strain was predicted at the

outer bending zone where the failure normally starts.

Figure 11: Longitudinal-Stress Distribution on the Sheet Thickness for DP 780 HY with w = 2t and the Final Punch Stroke

The stress distributions before and after springback of DP 780 HY were compared in Figure 12. The maximum stress was predicted at

the inner bent area as shown in Figure 12(a). The residual stress was predicted to remain on the bent sheet, as shown in Figure 12(b),

after removing the punch. As shown in Figure 12(b), the residual stress was predicted to be non-uniform along the width of sample.

This implies that the elastic recovery is different between the middle zone and the both ends of sheet width.

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Figure 12: Stress Distribution before and after Springback for DP 780 HY with w = 2t

The relative springback was compared between experiment and FEM for three different AHSS and two die opening lengths, as shown

in Figure 13. The larger die opening length (w = 8t) showed more springback compared to w = 2t. TRIP 780 showed relatively

smaller springback compared to DP 780 and 780 HY materials at both die opening lengths. The FE models showed good correlation

with experimental result of DP 780 at w = 2t; however, other cases for DP 780 HY and TRIP 780 showed a maximum 2% relative

springback difference between FEM and experiments.

Figure 13: Comparison of Springback between Experiments (RD) and FE Predictions for AHSS

3.3 Evaluation of Springback by using the S-Rail Stamping Test and FEA

Preliminary stamping trials were conducted with AKDQ steels to understand the material behaviors in S-rail stamping. In addition,

preliminary FE simulations of S-rail stamping were conducted to predict the maximum thinning for AKDQ and DP 780 materials.

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The S-rail test setup was installed in a 160-ton hydraulic press at OSU-CPF, as shown in Figure 14. The optimal geometry of the

initial sheet blank was determined from the previous stamping experiences with this tooling at Swerea-IVF which owns this tooling.

A initial blank geometry and a desirable stamping geometry are given in Figure 14.

Figure 14: Picture of S-Rail Stamping Test Setup at ERC/NSM-OSU and the CAD Models of Initial and Desirable Geometries of S-Rail Part

In the stamping test and FEA for AKDQ, the blank holder force of 90 kN was used. In the FE model, the coefficient of friction was

assumed as 0.13 and the punch stroke was set to be 25 mm, as measured in experiments. The FE model predicted the maximum

thinning to be about 11.3% and actual test showed no cracking and wrinkling on the part.

The overall shape of the AKDQ stamping was compared to the FEM predicted shape, as shown in Figures 15 and 16. However, the

thinning distribution on the stamped part was not made with FE predictions. With reliable measurement results from the coordinate

measurement machine (CMM) at OSU, detailed comparisons at selected cross sections will be made in terms of channel opening,

twisting, and side-curl in future work.

Figure 15: Comparison of AKDQ Stamping Shapes between Experiment and FEM

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Figure 16: Comparison of AKDQ Stamping Shapes between Experiment and FEM (Bottom View)

Preliminary FE simulations were conducted to know whether AHSS materials can be tested with the S-rail stamping test. Figure 17

showed the thinning distribution of DP 780 (initial thickness = 1 mm) predicted by FEM. The same DP 780 material properties

obtained from tensile and biaxial bulge tests were used for the FE simulations. The coefficient of friction (COF) was assumed to be

0.13 and the blank holder force was assumed to be 120 kN. FEM predicted the maximum thinning of 10%. Considering the

formability results of DP 780 (please refer Table 1), this would be marginably okay. To further reduce the maximum thinning in

experiments, the following recommendations can be taken as future work:

• Use better lubricant (reduce the coefficient of friction)

• Modify the initial blank geometry to reduce the maximum thinning at stretch flanging and shrink flanging areas

• Control the blank holder force without increasing springabck

Figure 17: FE Prediction of DP 780 (t0 = 1 mm) S-Rail Part

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3.4 S-rail Stamping Simulations with Constant and Variable Elastic Modulus for DP980

A case study was conducted by FEM of S-rail stamping with DP980 to demonstrate the effect of variable elastic modulus on

springback prediction. The relationship between the elastic modulus for DP980 and the plastic strain increase was obtain from

literature [49] as shown in Figure 18. The selected curve for DP980 was modeled with a commercial FE code, LS-DYNA. The sheet

thickness was modeled as 0.8 mm to accommodate in S-rail stamping tools (the clearance between the punch and die is 1.1 mm).

Figure 18: Variation of the Apparent Young’s Modulus (EA) with tru strain in tensile test for DP steels (Courtesy of Cobo et al.

2009) [49]

Same inputs of hardening model, friction coefficient (0.13), binder force (120KN) were used in simulations. Two different elastic

modulus, a constant (207 GPa) elastic modulus versus variable elastic modulus (Figure 18), were defined in FE simulations.

The resultant displacement during springback of S-rail part is compared between constant modulus and variable modulus as shown in

Figure 19. The difference of maximum displacement between two elastic modulus models was predicted to be 16% and a variable

elastic modulus gave more severe springback compared to a constant elastic modulus model.

Figure 19: Springback simulation results of resultant displacement between constant elastic modulus and variable modulus

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To understand the amount of elastic recovery, the residual stress after springback was compared in Figure 20. As expected, variable

elastic modulus predicted about 620 MPa lower maximum residual stress compared to the constant elastic modulus as shown in Figure

20. This implies that the variable modulus model results in larger elastic recovery which corresponds to a larger springback

magnitude.

Two cross sections were selected for comparing the springback between both elastic modulus models as shown in Figure 21. These

sections were predicted to have maximum plastic strains in S-rail part by FEA. The three section profiles in cutting section 1 were

plotted together in Figure 22. The variable elastic modulus gave larger channel opening of S-rail part compared to the constant elastic

modulus model. The experimental validation is ongoing at OSU and more detailed results will be available in future publications.

Figure 20: Springback simulation results of residual stress between constant elastic modulus and variable modulus

Figure 21: Selected sections for sprinback comparison

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Figure 22: Comparison of cross section profile of S-rail part in cutting section 1

4.0 CONCLUSIONS

The following conclusions can be drawn from this project:

• From the cyclic tensile test, DP 600 and 304 stainless steel showed 10 and 20%, respectively, decreases of elastic modulus as

the plastic strain increased.

• The material properties (elastic modulus, hardening curve, and anisotropy coefficients) obtained from the tensile test and

biaxial bulge test were used for FE simulations of V-bend test and S-rail flanging test.

• In the V-bend test, the load-displacement curve showed good agreements with FE predictions.

• In the V-bend test, TRIP 780 showed relatively smaller springback compared to DP 780 and 780 HY materials at both die

opening lengths.

• The relative springback of V-bend test was compared with FE predictions. They showed some discrepancies between

experiments and FE predictions. Therefore, material models (by including variable elastic modulus and improved hardening

model) should be further improved in future work.

• S-rail stamping trials with AKDQ gave good correlations to FEM predicted geometry without tearing or wrinkling.

• Preliminary FE simulations for S-rail stamping showed good feasibility to test AHSS without excessive thinning.

• Springback simulations were conducted for DP980 S-rail part with constant and variable elastic modulus. The variable elastic

modulus gave the higher magnitude of springback compared to the constant elastic modulus model.

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5.0 ACKNOWLEDGEMENT

This study was conducted with support from the State of Ohio, Department of Development and Thomas Edison Program, which

provided funding in support of Edison Technology and Industry Center Services. The authors also sincerely thank Dr. Taylan Altan,

director of Center for Precision Forming and Dr. Boel Wadman, Project Manager of Swerea-IVF for their support and advices on this

joint cooperative research program. We also acknowledge Dr. Hariharasudhan Palaniswamy and Mr. Kyungbo Kim (former graduate

research associates at CPF) and Nimet Kardes (a graduate research associate at CPF) and Yurdaer Demiralp (a visiting scholar at CPF)

for their technical work of test results and analyses.

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