CN102052981B - Test device and test method for measuring residual stress of bent pipe - Google Patents

Abstract

The invention relates to a test device and test method for measuring residual stress of a bent pipe and belongs to the technical field of experimental mechanics and residual stress measurement. In the method provided by the invention, the digital speckle correlation technique is combined with the drilling technique, and the method comprises the following steps: using a CCD (charge coupled device) camera to take photos of the bent pipe before and after the bent pipe is drilled; utilizing the digital speckle technique to measure the stretched displacement of two ends of the front and back drilled round holes; and measuring the residual stress of the bent test piece with a confirmed principal stress direction, so as to acquire the residual stress. The digital speckle correlation technique used in the method refers to non-contact measurement. Compared with the traditional electrical testing method, the method has the advantage that the complex process of sticking a foil gauge each time is omitted, thereby being more convenient and simpler. For the measurement of the residual stress of the bent pipe, a column correcting process is added in the method provided by the invention as compared with the traditional method, thus the acquired result is more accurate.

Description

A kind of experimental provision and method of measuring the bend pipe unrelieved stress

Technical field

The present invention relates to relevant the combining of a kind of digital speckle and measure the apparatus and method of bend pipe unrelieved stress, belong to Experimental Mechanics, unrelieved stress detection technique field with drilling technique.

Background technology

Bend pipe will receive from various external force effects and influence in the process that is processed by straight tube; After these external force disappear, will produce plastic yield in the member, the influence of plastic yield makes the effect thereupon complete obiteration of external force to member, still has partial action and influence to remain in the member, thus remaining bigger unrelieved stress in the bend pipe.At present the mensuration of unrelieved stress is mainly used the electrical measurement boring method; To survey hole of brill on the member; Make the unrelieved stress of member around obtain discharging, record the burst size of strain through foil gauge in the hole, thus the anti-residual-stress value that pushes away; But the each measurement of this kind method all will be pasted foil gauge, and operation is comparatively loaded down with trivial details.The digital speckle correlation technique is a kind of based on body surface speckle image gray analysis, thereby obtains the novel optical measurement method of object of which movement and deformation information.Demand developing the relevant method that combines with drilling technique of a kind of digital speckle urgently, can detect unrelieved stress more conveniently.

Summary of the invention

The purpose of this invention is to provide a kind of experimental provision and method of measuring the bend pipe unrelieved stress,, it can accurately be measured the unrelieved stress of the known bend pipe test specimen of principal direction of stress through the relevant method that combines with drilling technique of digital speckle.

Technical scheme of the present invention is following:

A kind of experimental provision of measuring the bend pipe unrelieved stress is characterized in that: this device comprises CCD camera, support, motorized precision translation stage, the computing machine that contains the digital speckle related software, drilling equipment, illuminating cold light source, and the anchor clamps that are used for fixing test specimen; Described CCD camera and cold light source are arranged on the motorized precision translation stage top, and are fixed on the support; Support is left and right sides translation on motorized precision translation stage; The anchor clamps of said fixedly test specimen are arranged on an end of motorized precision translation stage; The CCD camera is connected with computing machine through operation circuit with motorized precision translation stage.

Utilize the present invention can realize the measurement of bend pipe unrelieved stress, it is characterized in that this method comprises the steps:

1) sprays chequered with black and white lacquer spot on the bend pipe surface;

2) utilize anchor clamps that bend pipe is fixed, the planar horizontal that makes the tested point place on the test specimen up;

3) the CCD camera is aimed at tested point, regulate the position and the focal length of this CCD camera, make tested point in the middle of the CCD viewing field of camera, become distinct image, demarcate each millimeter corresponding what pixels in image, clap a photos;

4) use the motorized precision translation stage traversing carriage, the CCD camera is removed, bore an aperture at the tested point place, the CCD camera is accurately resetted, clap a photos again;

5) calculate the directions X of boring front and back and the displacement field of Y direction with the digital speckle related software, draw the opening displacement on two vertical direction of little bore edges;

6) utilize the anti-unrelieved stress that pushes away place, test specimen measured point of formula by opening displacement:

Suppose W ₀And W ₉₀Be respectively the opening displacement of directions X and Y direction, calculating the opening displacement zone is r to the distance of treating the gaging hole center, then directions X principle stress σ _X, Y direction principle stress σ _YBe respectively:

${\mathrm{\σ}}_X=E\frac{{\mathrm{BW}}_0-{\mathrm{BW}}_{90}-{\mathrm{DW}}_0-{\mathrm{DW}}_{90}}{2(\mathrm{BC}-\mathrm{AD})},$ ${\mathrm{\σ}}_Y=E\frac{{\mathrm{AW}}_0-{\mathrm{AW}}_{90}-{\mathrm{CW}}_0-{\mathrm{CW}}_{90}}{2(\mathrm{AD}-\mathrm{BC})}$

Wherein E is the elastic modulus of member, and A, B, C, D calculate with following formula:

$A=\frac{a^2}{\mathrm{Rr}}(1+v)$

$B=\frac{a^2}{\mathrm{Rr}}(1+v)+\frac{{\mathrm{\πa}}^2\sqrt{3(1-v^2)}}{4\mathrm{Rh}}[(\frac{r}{R}+\frac{a^2}{\mathrm{Rr}}-\frac{26}{5}\frac{a}{R})-v(\frac{r}{R}-\frac{a^2}{\mathrm{Rr}}-\frac{26}{5}\frac{a}{R})]$

$C=4\frac{a^2}{\mathrm{Rr}}-\frac{a^4}{{\mathrm{Rr}}^3}-v\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="Rr"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">Rr</figure-callout>}}^3}+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="Rr"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">Rr</figure-callout>}}^3}+4\frac{a^2}{\mathrm{Rr}}+\frac{r}{R}-\frac{29}{5}\frac{a}{R})+v(\frac{r}{R}-\frac{a^4}{{\mathrm{Rr}}^3}-5\frac{a}{R})]$

$D=-4\frac{a^2}{\mathrm{Rr}}+\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="Rr"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">Rr</figure-callout>}}^3}+v\frac{a^4}{{\mathrm{Rr}}^3}-\frac{{3\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="Rr"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">Rr</figure-callout>}}^3}+4\frac{a^2}{\mathrm{Rr}}+\frac{r}{R}-\frac{29}{5}\frac{a}{R})-v(\frac{r}{R}-\frac{a^4}{{\mathrm{Rr}}^3}-5\frac{a}{R})]$

Wherein: v is the Poisson ratio of member, and a is a boring radius, and R is the pipe radius, and h is the pipe wall thickness.

The present invention compared with prior art has the following advantages and the high-lighting effect: the digital speckle correlation technique that the present invention adopts is a non-cpntact measurement, compares with traditional electric measuring method, has saved the loaded down with trivial details operation that at every turn all will paste foil gauge, and is more convenient simple; For the measurement of bend pipe unrelieved stress, the present invention compares classic method and has added the cylinder correction term, makes the result who obtains more accurate.

Description of drawings

Fig. 1 is the structural principle synoptic diagram of apparatus of the present invention.

Fig. 2 is the zoning synoptic diagram.

Fig. 3 (a) is the displacement field of the directions X before and after the boring among the embodiment.

Fig. 3 (b) is the displacement field of the Y direction before and after the boring among the embodiment.

Among the figure: the 1-CCD camera; The 2-support; The 3-motorized precision translation stage; The 4-computing machine; The 5-drilling equipment; The 6-test specimen; The 7-cold light source; The 8-anchor clamps; F-boring back speckle is destroyed imponderable zone; G-holes regional; H-zoning H; I-zoning I; J-zoning J; K-zoning K.

Embodiment

Further specify concrete structure of the present invention, principle of work, the course of work below in conjunction with accompanying drawing, but should not limit protection scope of the present invention with this.

Fig. 1 is the structural principle synoptic diagram of this test lateral bending pipe unrelieved stress device.This device comprises CCD camera 1, support 2, motorized precision translation stage 3, the computing machine 4 that contains the digital speckle related software, drilling equipment 5, illuminating cold light source 7, and the anchor clamps 8 that are used for fixing test specimen; Described CCD camera 1 is arranged on the motorized precision translation stage top with cold light source 7, and is fixed on the support 2; Support is left and right sides translation on motorized precision translation stage; The anchor clamps 8 of said fixedly test specimen are arranged on an end of motorized precision translation stage; CCD camera 1 is connected with computing machine 4 through operation circuit with motorized precision translation stage 3.

The digital speckle related software can be referring to document Yao, X.F., Meng; L.B., Jin, J.C.; Yeh; H.Y.Full-fielddeformation measurement of fiber composite pressure vessel using digital specklecorrelation method.Polymer Testing 24,245-251,2005.

Method provided by the invention comprises the steps:

1) sprays chequered with black and white lacquer spot on the bend pipe surface;

2) utilize anchor clamps that bend pipe is fixed, the planar horizontal that makes the tested point place on the test specimen up;

3) the CCD camera is aimed at tested point, regulate the position and the focal length of this CCD camera, make tested point in the middle of the CCD viewing field of camera, become distinct image, demarcate each millimeter corresponding what pixels in image, clap a photos;

4) use the motorized precision translation stage traversing carriage, the CCD camera is removed, bore an aperture at the tested point place, the CCD camera is accurately resetted, clap a photos again;

5) calculate the displacement field before and after holing with the digital speckle related software, draw the opening displacement on two vertical direction of little bore edges, Fig. 2 is the synoptic diagram of boring back CCD camera image; Area E is the boring zone; The centre distance drill center of zone A-D is r, with the displacement of digital speckle correlation technique zoning H-K, if X is the bend pipe axial direction; Y is a bend pipe hoop direction, then the axial opening displacement W of aperture _XFor regional J average displacement subtracts regional H average displacement, aperture hoop opening displacement W _YFor the area I average displacement subtracts regional K average displacement.

6) utilize the anti-unrelieved stress that pushes away place, test specimen measured point of formula by opening displacement:

Bend pipe upper surface place principal direction of stress is along directions X and Y direction, can be approximated to be principal direction of stress vertically with the cylindrical tube of hoop.Theoretical according to opening in shell, under Fig. 2 circular cylindrical coordinate, the ρ direction that boring produces and the extra-stress σ of θ direction _ρAnd σ _θFor

${\mathrm{\&sigma;}}_{\mathrm{\&rho;}}=-\frac{1}{2}\frac{a^2}{r^2}({\mathrm{\&sigma;}}_X+{\mathrm{\&sigma;}}_Y)+(-2\frac{a^2}{r^2}+\frac{3}{2}\frac{a^4}{r^4})({\mathrm{\&sigma;}}_X-{\mathrm{\&sigma;}}_Y)\cos 2\mathrm{\&theta;}$ ①

$+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{32\mathrm{Rh}}[4(1-\frac{a^2}{r^2}){\mathrm{\&sigma;}}_Y+(3\frac{a^4}{r^4}-4\frac{a^2}{r^2}+1)({\mathrm{\&sigma;}}_X-{3\mathrm{\&sigma;}}_Y)\cos 2\mathrm{\&theta;}]$

${\mathrm{\&sigma;}}_{\mathrm{\&theta;}}=\frac{a^2}{{2r}^2}({\mathrm{\&sigma;}}_X+{\mathrm{\&sigma;}}_Y)-\frac{{3a}^4}{{2r}^4}({\mathrm{\&sigma;}}_X-{\mathrm{\&sigma;}}_Y)\cos 2\mathrm{\&theta;}$ ②

$+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{32\mathrm{Rh}}[4(1+\frac{a^2}{r^2}){\mathrm{\&sigma;}}_Y-(1+3\frac{a^4}{r^4})({\mathrm{\&sigma;}}_X-{3\mathrm{\&sigma;}}_Y)\cos 2\mathrm{\&theta;}]$

Wherein v is the elastic modulus of member, and a is a boring radius, and R is the pipe radius, and h is the wall thickness of pipe, and r is the distance of digital speckle zoning centre distance drill center, σ _XAnd σ _YFor the antecurvature tubular axis of perforate not to the unrelieved stress of hoop.

What according to formula 1. and 2., boring produced along the axial additional strain of aperture is:

${\mathrm{\&epsiv;}}_{\mathrm{\&rho;}}=\frac{1}{E}({\mathrm{\&sigma;}}_{\mathrm{\&rho;}}-{\mathrm{v\&sigma;}}_{\mathrm{\&theta;}})$

$=\frac{1}{E}\left\{\right[-\frac{1}{2}\frac{a^2}{r^2}({\mathrm{\&sigma;}}_X+{\mathrm{\&sigma;}}_Y)-v\frac{a^2}{{2r}^2}({\mathrm{\&sigma;}}_X+{\mathrm{\&sigma;}}_Y)]$

$+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{32\mathrm{Rh}}[4(1-\frac{a^2}{r^2}){\mathrm{\&sigma;}}_Y-4v(1+\frac{a^2}{r^2}){\mathrm{\&sigma;}}_Y]$ ③

$+[(-2\frac{a^2}{r^2}+\frac{3}{2}\frac{a^4}{r^4})({\mathrm{\&sigma;}}_X-{\mathrm{\&sigma;}}_Y)+v\frac{{3a}^4}{{2r}^4}({\mathrm{\&sigma;}}_X-{\mathrm{\&sigma;}}_Y)]\cos 2\mathrm{\&theta;}$

$+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{32\mathrm{Rh}}[(3\frac{a^4}{r^4}-4\frac{a^2}{r^2}+1)({\mathrm{\&sigma;}}_X-3{\mathrm{\&sigma;}}_Y)+v(1+3\frac{a^4}{r^4})({\mathrm{\&sigma;}}_X-3{\mathrm{\&sigma;}}_Y)]\cos 2\mathrm{\&theta;}\}$

Wherein E is the elastic modulus of member.Formula 1,3 in 3. is a planar solution; 2,4 is the cylinder correction term; With 1,3 from infinite distant place integration, 2,4 at infinity also have small value, the main influence that boring back unrelieved stress discharges is in the zone apart from the 5-8 times of boring radius in center, hole; So 2,4 since 5 times of boring radius place integrations, then the opening displacement at aperture two ends is:

$W_{\mathrm{\&rho;}}=\frac{1}{E}\{\frac{a^2}{r}(1+v){\mathrm{\&sigma;}}_0$

$+[\frac{a^2}{r}(1+v)+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{4\mathrm{Rh}}[(r+\frac{a^2}{r}-\frac{26}{5}a)-v(r-\frac{a^2}{r}-\frac{26}{5}a)\left]\right]{\mathrm{\&sigma;}}_{90}$ ④

$+[4\frac{a^2}{r}-\frac{a^4}{r^3}-v\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+4\frac{a^2}{r}+r-\frac{29}{5}a)+v(r-\frac{a^4}{r^3}-5r)\left]\right]{\mathrm{\&sigma;}}_0\cos 2\mathrm{\&theta;}$

$+[-4\frac{a^2}{r}+\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+v\frac{a^4}{r^3}-\frac{{3\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+4\frac{a^2}{r}+r-\frac{29}{5}a)-v(r-\frac{a^4}{r^3}-5a)\left]\right]{\mathrm{\&sigma;}}_{90}\cos 2\mathrm{\&theta;}\}$

Suppose W ₀And W ₉₀Be respectively the opening displacement of bend pipe to be measured, simultaneous equations at and hoop axial apart from r place, center, hole:

$\left\{\begin{array}{c}{W}_0=W_{\mathrm{\&rho;}}|(\mathrm{\&theta;}=0)\\ W_{90}=W_{\mathrm{\&rho;}}|(\mathrm{\&theta;}=90)\end{array}\right.$ ⑤

Axial principal stress σ then _X, hoop principle stress σ _YBe respectively

${\mathrm{\&sigma;}}_X=E\frac{{\mathrm{BW}}_0-{\mathrm{BW}}_{90}-{\mathrm{DW}}_0-{\mathrm{DW}}_{90}}{2(\mathrm{BC}-\mathrm{AD})},$ ${\mathrm{\&sigma;}}_Y=E\frac{{\mathrm{AW}}_0-{\mathrm{AW}}_{90}-{\mathrm{CW}}_0-{\mathrm{CW}}_{90}}{2(\mathrm{AD}-\mathrm{BC})}$ ⑥

Wherein E is the elastic modulus of member, and A, B, C, D coefficient are following:

$A=\frac{a^2}{r}(1+v)$

$B=\frac{a^2}{r}(1+v)+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{4\mathrm{Rh}}[(r+\frac{a^2}{r}-\frac{26}{5}a)-v(r-\frac{a^2}{r}-\frac{26}{5}a)]$

$D=4\frac{a^2}{r}-\frac{a^4}{r^3}-v\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}\left[(-\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+4\frac{a^2}{r}+r-\frac{29}{5}a)+v(r-\frac{a^4}{r^3}-5a)\right]$

$D=-4\frac{a^2}{r}+\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+v\frac{a^4}{r^3}-\frac{{3\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000045955790000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^3}+4\frac{a^2}{r}+r-\frac{29}{5}a)-v(r-\frac{a^4}{r^3}-5a)]$

Wherein v is the elastic modulus of member, and a is a boring radius, and R is the pipe radius, and h is the wall thickness of pipe, and r is the distance of digital speckle zoning centre distance drill center.

Embodiment:

Consider the displacement field of concrete situation a: Fig. 3 for digital speckle correlation computations gained before and after the boring; Wherein Fig. 3 (a) is the displacement field of directions X; Fig. 3 (b) is a Y direction displacement field; Then apart from the opening displacement apart from the r=1.7mm two ends at aperture center, directions X is 0.10 μ m, and the Y direction is 1.39 μ m.With boring radius a is 0.85mm, elbow radius R=12.5mm, and wall thickness h=5mm, elasticity modulus of materials E=210GPa, 6. material Poisson ratio v=0.3 brings formula into, and the directions X unrelieved stress is 101.0MPa, and Y direction unrelieved stress is 187.9MPa.The unrelieved stress Y direction of using traditional electrical measurement boring method to record identical test specimen is 105.4MPa, and directions X is 200.5MPa, and both results meet better.

Claims (1)

1. a method of measuring the bend pipe unrelieved stress is characterized in that this method comprises the steps:

1) sprays chequered with black and white lacquer spot on the bend pipe surface;

2) utilize anchor clamps that bend pipe is fixed, the planar horizontal that makes the tested point place on the bend pipe up;

3) the CCD camera is aimed at tested point, regulate the position and the focal length of this CCD camera, make tested point in the middle of the CCD viewing field of camera, become distinct image, demarcate each millimeter corresponding what pixels in image, clap a photos;

4) use the motorized precision translation stage traversing carriage, the CCD camera is removed, bore an aperture at the tested point place, the CCD camera is accurately resetted, clap a photos again;

5) calculate the directions X of boring front and back and the displacement field of Y direction with the digital speckle related software, draw the opening displacement on two vertical direction of little bore edges;

6) unrelieved stress of utilizing the anti-bend pipe of formula measured point to locate by opening displacement:

Suppose W ₀And W ₉₀Be respectively the opening displacement of directions X and Y direction, the distance of digital speckle zoning centre distance drill center is r, then directions X principle stress σ _x, Y direction principle stress σ _YBe respectively:

${\mathrm{\&sigma;}}_X=E\frac{{\mathrm{BW}}_0-{\mathrm{BW}}_{90}-{\mathrm{DW}}_0-{\mathrm{DW}}_{90}}{2(\mathrm{BC}-\mathrm{AD})},$ ${\mathrm{\&sigma;}}_Y=E\frac{{\mathrm{AW}}_0-{\mathrm{AW}}_{90}-{\mathrm{CW}}_0-{\mathrm{CW}}_{90}}{2(\mathrm{AD}-\mathrm{BC})}$

Wherein E is the elastic modulus of bend pipe, and A, B, C, D calculate with following formula:

$A=\frac{a^2}{\mathrm{Rr}}(1+v)$

$B=\frac{a^2}{\mathrm{Rr}}(1+v)+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{4\mathrm{Rh}}[(\frac{r}{R}+\frac{a^2}{\mathrm{Rr}}-\frac{26}{5}\frac{a}{R})-v(\frac{r}{R}-\frac{a^2}{\mathrm{Rr}}-\frac{26}{5}\frac{a}{R})]$

$C=4\frac{a^2}{\mathrm{Rr}}-\frac{a^4}{{\mathrm{Rr}}^3}-v\frac{a^4}{{\mathrm{Rr}}^3}+\frac{{\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{Rr}}^3}+4\frac{a^2}{\mathrm{Rr}}+\frac{r}{R}-\frac{29}{5}\frac{a}{R})+v(\frac{r}{R}-\frac{a^4}{{\mathrm{Rr}}^3}-5\frac{a}{R})]$

$D=-4\frac{a^2}{\mathrm{Rr}}+\frac{a^4}{{\mathrm{Rr}}^3}+v\frac{a^4}{{\mathrm{Rr}}^3}-\frac{{3\mathrm{\&pi;a}}^2\sqrt{3(1-v^2)}}{16\mathrm{Rh}}[(-\frac{a^4}{{\mathrm{Rr}}^3}+4\frac{a^2}{\mathrm{Rr}}+\frac{r}{R}-\frac{29}{5}\frac{a}{R})-v(\frac{r}{R}-\frac{a^4}{{\mathrm{Rr}}^3}-5\frac{a}{R})]$

Wherein: v is the Poisson ratio of bend pipe, and a is a boring radius, and R is the pipe radius, and h is the pipe wall thickness.

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