DETERMINATION OF CLAD PLATES RESIDUAL STRESSES BY X-RAY DIFFRACTION METHOD

Original scientific paper The paper elaborates the influence that clad procedure has on the level and nature of residual stresses in clad plates. There are three clad procedures applied, as follows: hot rolling, submerged arc welding (SAW) with strip electrode in two layers and explosion welding. Theoretical basics on residual stresses measured by x-ray diffraction are reviewed in the paper, with special emphasis put on problems of underclad cracking tendency. In all applied cladding procedures, usage of heat treatment by anealing resulted in the decrease of residual stresses values. However, transformation of commpresed stresses into tensile stresses in some cases was very unfavourable, if referring to the tendency of plating corrosion resistant steel to stress corrosion and to underclad cracking.


Introduction
Residual stresses occur during welding due to inhomogeneous temperature distribution.At the bonding interface, temperatures are significantly higher than in the base materials [1].It is also related to explosion welding process, due to partial conversion of elevated impact energy to heat, which may produce local melting or annealing close to the interface.During cooling, the regions near the cladded interface tend to contract while impeded by the surrounding base material.This may lead to elevated tensile stresses close to the welding interface with balancing compressive stresses throughout the base metal [1].The performance of cladded plates can be influenced by residual stresses formed during welding or post weld heat treatment (PWHT), which may cause dimensional instability during cutting or machining operations, as well as underclad cracking.In the case of dissimilar materials, residual stresses are increased by differences in elastic properties (separate module elasticity E and thermal expansion coefficient of the materials α).It is important to determine size and nature of residual stresses at plated construction with dissimilar steels.Knowledge about tensile residual stresses is essential because there is a possibility of cracking tendency of corrosion resistant steel to stress corrosion.Knowledge about compressive residual stresses and their influence on construction stability is also indispensable [2].
Underclad cracks are intergranular separations placed in the coarse-grained heat-affected zone of low-alloy steels below the weld-cladding overlay, whose dimensions are no less than about 3 mm deep and 3 mm long [3].Weld-overlay cladding with high-heat-input processes provides the susceptible microstructure and tensile residual-stress separately at weld passes overlapping.Postweld heat treatment provides the critical temperature region, usually between 600 and 650 °C, i.e. with low creep ductility [3].When depositing the first layer, a coarse-grained microstructure is generated in the HAZ.While depositing the second layer, the second fusion line is situated at the surface of the first layer.The coarse-grained zone microstructure is refined.In case of the incomplete refinesment, final product still contains areas with coarse-grained microstructure.When PWHT is applied, coarse-grained areas have tendency to potential intergranular underclad crack locations [4].

Materials and experiment plan
The experiment objective is to determine the influence of cladding procedure on the nature and values of residual stresses in plating stainless steel surfaces.The experiment plan of measuring residual stresses by x-ray diffraction is presented in Tab. 1. Dimensions of examined plates were 100 × 100 × δ mm.The base material ASTM A387 Gr.12 is delivered in normalised and the plating ASTM A240 TP304L in quenched state (Tab.2).Overlaying is performed in two beads using a device to prevent plate distortion.Afterwards, clad plate is examined by dye-penetrant testing with intention to dicover surface errors.Ultrasound method tandemtechnique with 70°-angle probes frequency 2 MHz is used with intention to discover under-cladding cracks caused by heat-affected zone (HAZ) reheating (Tab.3).Explosion cladded joint is produced by using a single cladding shot and parallel joining scheme.Distance between flayer and fixed plate was 10 mm with 20 mm thick explosive powder layer.Explosive materialammonite (85 % ammonium nitrates as oxidizer + 12 % explosive trinitrotoluene (TNT) + 3 % Al as fuel) in powder form is used with a standard commercial blasting cap no. 8 instantaneous as activator to detonate the explosive.Bond integrity is verified by using straightbeam ultrasonic inspection procedures.Specifications provided several acceptance criteria depending on customer's needs, the more stringent being 25 mm maximum length of any indication and 99 % minimum sound bond area.

The basic theory of residual stresses measurment by x-ray diffraction
This stress analysis technique is based on deformation crystals lattice measurement ∆d/d (Fig. 1).

Figure 1 Diffraction of x-rays by a crystal and Bragg's law
The x-rays of appropriate wavelength are used for measurements.Interference lines (h, k, l) are suported by special devices (camera photograph for reflected x-rays filming or diffractometer-goniometer with proportional and scintillation counter).At computing, elastomechanics equations are used.If residual stresses are of range size 10 Pa, distance between crystal lattice planes changes in relation to status without residual stresses for only a tenth of a thousandth part.Because of the stated, and if referring to guarantee satisfied sensitivity methods, diffractometers measuring at greater Braggs angles 2ϑ (near 180°) should be performed [5,6].According to the Bragg's law, it follows: where: λ -x-ray wavelength, d -distance between nearby crystal lattice planes, ϑ -angle between primary/reflected x-ray beam and crystal lattice planes.
Using the differentials Eq. ( 1) at λ = const.it follows: It confirms the fact that the crystal lattice planes distances change, causing doubled angle ϑ (Bragg's angle) to change.The x-ray diffraction measurement is technically limited to 5 ÷ 30 µm thick surfacing layer.If it is assumed that the stress in surfacing layer thickness direction is zero (0), there exist only main stresses on surface layer.Related to activity direction, the mentioned stresses σ 1 and σ 2 are in reciprocally perpendicular position.According to the above assumption, the relations between main stresses and deformation on the sample surfaces using Hooke's law are as follows: ( ) where: E -elasticity modulus, ν -Poisson's coefficient and ε -measured material sample deformation.
Furthermore, relations between stresses tensors and deformation tensors are defined by the following equation with parameters presented in Fig. 2. ( ) ( ) In direction determined by azimuth angle φ, and polar angle ψ, there is: At determination σ x two measurements of deformation change should be realized.If: d 0 − distance between crystal lattice planes at unstrained status; d ⊥ − distance between crystal lattice planes parallel with sample surface at strained status, and d φ,ψ − distance between crystal lattice planes that is normal to direction (φ,ψ) at strained status.
Deformation record as: followed by: ( ) (10) Due to the small changes of distance between crystal lattice planes caused by residual stresses, the following is roughly drawn: Since E and ν material properties are from Eq. (11) σ x residual stresses can be determined.
At determined reflection type Bragg's angles difference ∆ϑ 1 should be measured.
First, the vertical line on sample surface coincides with the axis of symmetry between primary and reflected x-ray beam.Then the measuring between normal line on sample surface and axis of symmetry is ψ angle.Measurement procedure is like that at determination σ x , but the sample should be rotated round its normal at 90° [8,9].
Residual stress σ y is determined from equation:

Description of diffractometer operation
Diffractometer is a special device used for measuring of all Bragg's angles x-rays reflection on crystals, with respect to precise position and intensity of Debye-Scherrer lines.Equipment is composed of three parts: xray source, goniometer and detector (Fig. 3).During the measuring process the angle is changed, i.e. vertical line on the sample surface and axis of symmetry between primary and reflected beams is close to ψ angle (Fig. 4).

Figure 3
Diffractometer working principle [9] At flat samples, allready for ψ = 0 primmary x-ray beams divergency causes unsymmetrical lines to expand and to move (Fig. 5).For primmary beam angle 2δ < 1, at measured sttresses, error is less than 10 MPa, which is technically acceptable.Divergence of primary x-ray beam could be eliminated by detectoric slits (Z1 and Z2) or by other technical solution.
Detector moves on gonimetric circle M and registers reflected x-ray beam intensity.The focusing condition is that x-ray source, surface plane of sample U and primmary slits A are situated on circle K (Figs. 3 ÷ 5).
This focused circle during focusing permanently changes its diameter.In this way, the focus place from point A moves to point A', which is expanding lines on detectors.One solution is that detector slits shoud be moved to the distance AA' (Fig. 4), but such correction is Technical Gazette 22, 6(2015), 1533-1538 rarely used as a procedure, so the defocusing effects will be eliminated in other ways.Interference lines for different Bragg's angles ϑ and different ψ angles in reflection area are recorded as well as interference lines position.At ψ diffractometer, compared to Ω -diffractometer, which has common ϑand ψ -axis, these axes are reciprocally perpendicular (Fig. 6).

Measurements specification and their characteristics
From cladded plates dimensions 100 × 100 × δ, tested samples with dimensions 20 × 30 mm are cut by mechanical procedure.This dimension was acceptable for special constructed sample holder.
Since the penetrating power of x-rays used for diffraction is small, the surface preparation is very important, since it should be smooth.This is achieved by surface grinding followed by mechanical polishing.The main limitation of that method is that it can be used only for the evaluation of surface residual stresses.If stress distribution through the thickness is required, surface layers have to be removed by electropolishing [8,10].
Measurement of residual stresses is on interference lines movement at family of planes (311) based on surface centric crystal latice of γ-phase.At measurements, angle ψ between a normal on sample surface and symmetry axis between primary and reflected x-rays is changed in area 0° ÷ 50°.
As the angle 2ϑ should be as large as possible, with intention to obtain sufficient accuracy, aproximatelly 140° angle is for interference (311).
As mentioned, horizontal goniometer with Cu-anode is used for residual stresses analysis with the following parameters: -anoda voltage 35 kV, -anoda current 14 mA, -primary screen 0,5°, -graphite monocromator Kα', -detector voltage 1,1 kV, -discrimination stress 1,3 V, -attenuation amplifier 5 x.-wavelength characteristics line Kα 1 0,15405 nm.Therefore, electronic impulse counter determines the position of interference lines maximum.The angle (2ϑ) firstly increased with step of 0,02° (at first three examined samples) and subsquently of 0,05° (at other three examined samples).Firstly, measurement is performed on samples cladded by strip electrodes SAW.Afterwards, cladded samples are submitted to the xray diffraction measurements by explosion welding, as well as by hot rolling.In the interval of 2° peak area of interference line, the quadratic parabole is used as approximation.The position of top parabole is considered as a maximum interference line.After establishing angles at interference lines maximum (maximum impulse numbers), residual stresses normal to direction (φ,ψ) are calculated by using the Eq. ( 13):  Tab. 5 presents related values.Graphical presentation of calculated residual stresses on (2ϑ) at maximal impulse number (interference lines maximum) is shown in Fig. 9.

Conclusions
In all applied cladding procedures with heat reatment by annealing a drop of residual stresses was determined.Type of plating procedure has a significant influence on the value of residual stresses.
Heat treatment has significant influence on range and nature of plating surface residual stresses, as present at specimens plated by welding (SAW) with electrodes in two beads.The transformation of compressed stresses into tensile stresses is very unfavourable if respecting the tendency of austenitic corrosion resistant steel to stress corrosion cracking.When PWHT is applied, base metal coarse grained areas and residual stresses changing into tensile have the tendency of potential intergranular underclad cracks.

Figure 2
Figure 2 Coordinate system at deformation determination and residualstresses on sample surface by x-ray diffraction technique[7]

Figure 4
Figure 4Focus movement from point A in A' at sample rotation for angle ψ[7,8]

Figure 7 4 4
Figure 7 Photographic presentation of ψ-principle diffractometer Siemens Kristaloflex -4 4 Measuring results and their analysis Since the interference line (311) is extended, determination of maximum line position is relatively serious.Due to precision, maximum intensity lines are aproximated by polynomial equation (Tab.4): y = ax 2 + bx + c, where the function top is: x = −b/2a.Therefore, electronic impulse counter determines the position of interference lines maximum.The angle (2ϑ) firstly increased with step of 0,02° (at first three examined samples) and subsquently of 0,05° (at other three

Figure 8
Figure 8 Graphical presentation of maximum intensity lines for no-heat-treated sample cladded by hot rolling Fig. 8 graphically presents maximum intensity lines for sample plated by hot rolling, derived from impulses data counted out and approximation function with maximum at 139,18° for ψ = 50° and φ = 0°.

Figure 9
Figure 9 Graphic review of calculated residual stresses values σx and σy on sample plated by austenitic corosion resistant steel

Table 1
Plan of experiments referring to residual stresses measurement

Table 2
Chemical and mechanical properties of the base materials

Table 4
Review of approximations function coefficients for y = ax 2 + bx + c, a function max.x = −b/2a

Table 5
Review of measured characteristics and x-ray diffraction measurements on residual stresses values