Fracture Strength Determination of Maraging Steel Rocket Motor Cases a Comparative Study ofAnalytical and Experimental Data

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Fracture Strength Determination of Maraging Steel Rocket Motor Cases a Comparative Study ofAnalytical and Experimental Data

Sreedevi Lekshmi

Master Student, Department of Civil Engineering, Sree Buddha College of Engineering,

Pattoor, Kerala, India

Anup Joy

Assistant Professor, Department of Civil Engineering, Sree Buddha College of Engineering,

Pattoor, Kerala, India

Abstract Maraging steels are greatly employed for the fabrication of rocket motor cases because of its high strength and fracture toughness. They are low carbon, high nickel, iron base alloys. Maraging steels can be easily machined, formed and welded. It has the composition of 18% Ni, 8% Co, and 5% Mo as a primary alloying element. Based on 0.2% proof stress levels, namely 200, 250, 300 and 350ksi, maraging steel can be classified as M200, M250, M300 and M350. High strength is obtained by ageing at 900 against the heat treatment used for other high strength alloys. Defects like cracks or flaws are developed in this material during fabrication process. Cracks generally have sharp edges and therefore sensitive for initiation of crack growth and fracture. In this paper, a procedure is presented to determine the failure load of a structural component in the presence of crack using an ASTM procedure. Fracture strength plays a vital role in determining critical stress intensity factor for any structural component. Equation for the determination of fracture strength of maraging steel is presented. The relationship between failure strength and critical stress intensity factor is briefly discussed. A limited number of surface cracked tension specimens made of maraging steel material having different width and crack sizes are used to derive fracture strength. The analytical results of fracture strength are determined using fracture parameters of maraging steel. Fracture strength obtained from test data are compared with analytical results and the relative error is presented. Failure assessment diagram in terms of critical stress intensity factor and failure stress is presented. Results are discussed.

Keywords- Maraging steel, Fracture strength, Crack size, Motor cases, Critical stress intensity factor, Surface cracked tension specimen, Failure assessment diagram.

  1. INTRODUCTION

    Maraging steel is currently being used for construction of space vehicle pressure vessels. It possess superior properties like high strength and toughness due to a combination of two solid state reactions, MAR + AGING, meaning martensitic transformation and subsequent ageing. It has the composition of 18% Ni, 8%Co and 5% Mo as a primary alloying element. Resistance of such high strength materials is sensitive to

    presence of crack like defects. The specified mechanical properties are:

    Plane strain fracture toughness, KIC 90MPa Yield strength, ys 1725 MPa

    Ultimate tensile strength, ult 1765 MPa Weld efficiency 90%

    The significant parameters to specify the critical crack size in structure are the applied load levels, the fracture toughness, the location of crack and its orientation. The theoretical determination of failure load and especially the failure process of flawed (in the case notched or initially cracked) structural components is indispensable in the performance of safety analysis. In addition to the generally very complex and expensive FEM, approximate analytical methods have been developed to assess the load bearing capacity of flawed structural components with a relatively low cost and computational time.

  2. FRACTURE STRENGTH OF CENTER CRACKED TENSILE SPECIMENS

    Several structural analysis method to predict the fracture behavior of cracked structural components were explained in detail by various researchers. Several fracture analysis methods to predict the fracture behavior of flawed structural components used in an experimental and predictive round robin conducted in 1970-80 by American Society for Testing Materials (ASTM) Task Group E 24.06.02 are : Linear elastic fracture mechanics (LEFM) corrected for size effects or plastic yielding; Equivalent energy; The Two-parameter criterion (TPFC); The deformation plasticity failure assessment diagram (DPFAD); The theory of ductile fracture; The KRcurve with the Dugdale model; An effective KR curve derived from residual strength data; The effective KR- curve with a limit load condition; Limit-load analyses; A two-dimensional finite element analysis using a critical crack

    tip-opening displacement criterion with stable crack growth; A three-dimensional finite element analysis using a critical crack- front singularity parameter with a stationary crack.

    In this paper, equation for fracture strength for a finite width tension plate containing central surface crack is presented.

    The stress intensity factor (KI) for a finite width plate containing a center surface crack of length 2c and depth a as shown in fig. 1 is

    KI= (M (a)0.5) / (1)

    Here is the applied stress, is the flaw shape parameter, M is the magnification factor, W is the width of the plate and t is the thickness of the plate.

    The magnification factor (M), finite width correction factor (fw), flaw shape parameter () in terms of the crack depth (a), half the crack length (c), width (W) and thickness (t) are

    M = Mefw ; Me = M1 + ( (c/ a) 0.5- M1 (a/t )q M1 = 1.13-0.1 (a/c); for ac

    M1 = (1+ 0.03 (a/c); for ac;

    2 = 1+ 1.464 (a/c)1.65 ; for <

    2 = 1+ 1.464 (c/a)1.65 ; for ;

    fw = sec( ); q = 2+ 8 (a/c)3

    the results are compared with the test data. Equation for failure load is as follows:

    Failure load,

    Pmax = 0.815BW ult (1 – a0/W)2 (2 +a0/W)-1 {0.3927+ 0.0402

    (a0/W) + 0.6268 (a0/W)2} (2)

    TABLE 1 FAILURE LOAD PMAX OF THE M250 GRADE MARAGING STEEL CT SPECIMENS

    ult (MPa

    W

    B

    a0

    Pmax (test)

    Pmax (eqn 2)

    1859

    14.98

    7.62

    7.720

    9.48

    9.31

    1761

    15.00

    7.62

    7.377

    9.28

    9.55

    1760

    15.02

    7.62

    7.440

    9.04

    9.45

    1798

    14.98

    7.62

    7.486

    9.09

    9.49

    1791

    15.01

    7.62

    7.520

    9.19

    9.43

    1843

    15.64

    7.80

    8.570

    9.21

    8.76

    1782

    15.59

    7.80

    7.788

    10.4

    10.0

    1782

    15.62

    7.80

    7.833

    10.3

    9.98

    1821

    15.54

    7.80

    7.747

    10.7

    10.3

    1790

    15.56

    7.79

    7.147

    11.5

    11.4

    1766

    15.61

    7.80

    7.903

    9.65

    9.73

    1781

    15.55

    7.80

    7.660

    11.0

    10.2

    1781

    15.54

    7.80

    p>7.742

    10.0

    10.0

    1815

    15.62

    7.80

    7.740

    10.7

    10.4

    1793

    15.60

    7.79

    7.917

    10.3

    9.82

    1846

    15.63

    7.81

    8.080

    10.4

    9.83

    1763

    15.57

    7.83

    8.045

    10.0

    9.38

    1790

    15.57

    7.80

    8.152

    9.90

    9.30

    1796

    15.61

    7.79

    7.890

    11.0

    9.91

    1817

    15.59

    7.80

    7.223

    11.4

    11.5

    1829

    15.61

    7.80

    7.892

    10.5

    10.1

    1829

    15.60

    7.80

    8.175

    9.82

    9.47

    1780

    15.58

    7.80

    7.620

    10.9

    10.4

    1821

    15.67

    7.81

    7.703

    9.88

    10.6

    1878

    15.63

    7.80

    7.741

    10.3

    10.8

    1847

    15.64

    7.79

    7.713

    10.9

    10.6

    1842

    15.64

    7.79

    7.333

    11.9

    11.5

    1872

    15.56

    7.78

    7.170

    11.2

    11.9

    1822

    15.54

    7.82

    8.123

    9.90

    9.46

    1814

    15.59

    7.82

    7.868

    9.90

    10.1

    ult (MPa

    W

    B

    a0

    Pmax (test)

    Pmax (eqn 2)

    1859

    14.98

    7.62

    7.720

    9.48

    9.31

    1761

    15.00

    7.62

    7.377

    9.28

    9.55

    1760

    15.02

    7.62

    7.440

    9.04

    9.45

    1798

    14.98

    7.62

    7.486

    9.09

    9.49

    1791

    15.01

    7.62

    7.520

    9.19

    9.43

    1843

    15.64

    7.80

    8.570

    9.21

    8.76

    1782

    15.59

    7.80

    7.788

    10.4

    10.0

    1782

    15.62

    7.80

    7.833

    10.3

    9.98

    1821

    15.54

    7.80

    7.747

    10.7

    10.3

    1790

    15.56

    7.79

    7.147

    11.5

    11.4

    1766

    15.61

    7.80

    7.903

    9.65

    9.73

    1781

    15.55

    7.80

    7.660

    11.0

    10.2

    1781

    15.54

    7.80

    7.742

    10.0

    10.0

    1815

    15.62

    7.80

    7.740

    10.7

    10.4

    1793

    15.60

    7.79

    7.917

    10.3

    9.82

    1846

    15.63

    7.81

    8.080

    10.4

    9.83

    1763

    15.57

    7.83

    8.045

    10.0

    9.38

    1790

    15.57

    7.80

    8.152

    9.90

    9.30

    1796

    15.61

    7.79

    7.890

    11.0

    9.91

    1817

    15.59

    7.80

    7.223

    11.4

    11.5

    1829

    15.61

    7.80

    7.892

    10.5

    10.1

    1829

    15.60

    7.80

    8.175

    9.82

    9.47

    1780

    15.58

    7.80

    7.620

    10.9

    10.4

    1821

    15.67

    7.81

    7.703

    9.88

    10.6

    1878

    15.63

    7.80

    7.741

    10.3

    10.8

    1847

    15.64

    7.79

    7.713

    10.9

    10.6

    1842

    15.64

    7.79

    7.333

    11.9

    11.5

    1872

    15.56

    7.78

    7.170

    11.2

    11.9

    1822

    15.54

    7.82

    8.123

    9.90

    9.46

    1814

    15.59

    7.82

    7.868

    9.90

    10.1

    When the depth (a) of the crack is equal to the thickness (t), Eq 1 gives the stress intensity factor for finite width tension specimens having a center through crack. Equation 1 holds good for both through and surface crack tension specimens.

    Equating the fracture toughness (KIC) of the material to the stress intensity factor (KI), one can find the fracture strength (f) of a finite width plate containing a surface crack. Fracture strength (f) equation is given as follows:

    =

    2

    2

    [1 ( 2 ) ] for 2

    f ult

    33 f 3

    f= KIC / M()

    f= KIC / M()

    From this expression fracture strength of M250 and M300 maraging steel rocket motorcase surface cracked tension specimen is evaluated. The results are compared with available test data and presented in the table. Based on the three parameter relationship among critical stress intensity factor (Kmax), the fracture strength (f) and the ultimate strength (ult), failure analysis diagram is presented and one can easily understand the range of Kmax over f and ult. In addition to the determination of fracture strength, an attempt is made to determine the failure load of 30 CT specimens and

  3. IMPORTANCE OF KMAX AND F RELATIONSHIP

    Understanding the failure of materials plays an important role in the design and manufacturing process. When dealing with a specific material for a particular application, it I not clearly established whether plain strain fracture toughness (KIC) should be used or plane stress condition. The KIC seems to be important in heavy sections like forging or thick plate. This is the reason why plane strain fracture toughness is used in thick sectioal structural member in aerospace applications.

    ASTM-E561 suggests generation of a R-curve from through crack test coupens like CT specimens. It should be noted KIC is geometry dependent where as R-curve is considered to be a material property independent of geometry. Therefore R-curve of material will be useful for the accurate determination of critical load of the through cracked specimen. For part through cracked configurations, fracture strength estimations are not possible directly from the R-curve of the material because the part through crack has 2 dimensions, namely crack length and its depth. In such situations, development of a relationship between the failure stress and the stress intensity factor at failure will be useful for fracture strength evaluation of cracked configurations.

    Rao et al derived a relation between the stress intensity factor and corresponding stress at failure for cracked configurations using crack-growth resistance curve (R-curve) of the material from CT specimens. The failure stress decreases with the increase of crack size. When the crack size is negligibly small, failure stress tends to the ultimate strength of the material. Since the stress intensity factor (KI) is a function of load, geometry and crack size, it is more appropriate to have a relationship between stress intensity factor at failure Kmax and the failure stress from the fracture data o cracked specimens and this is useful for fracture strength evaluation of flawed configuration.

    The relationship between Kmax and f can be of the form Kmax = KF {1-m (f/ ult) (1-m) (f/ ult)p}

    Where, f is the failure stress normal to the direction of the crack in a body and u is the normal stress required to produce a plastic hinge on the net section. For centre crack tension specimen, failure stress is equal to ultimate stress of the material. For the pressurized cylinders, failure stress is the hoop stress at the failure pressure of the flawed cylinder and ultimate stress is the hoop stress at failure pressure of an unflawed cylinder. In the above equation, KF, m and p are fracture parameters derived from fracture test data. The above equation is known as 3 parameter fracture criterion which was derived from the conventional 2 parameter criteria. It is a well known fact that the tensile strength of a specimen decreases with increasing crack size. If the failure stress is less than the yield stress, then there exists a linear relationship between f and Kmax. For small sizes of cracks where ys <f <u, the relationship between between fand Kmax is expected to be non linear. f is the 0.2% proof stress or yield stress of the material.

    Fig.1. Finite width tension plate containing a center surface crack

    Understanding the failure of materials plays an important role in the design and manufacturing process. When dealing with a specific material for a particular application, it is not clearly established whether plane strain fracture toughness (KIC) should be used for plane stress condition. The KIC seems to be important in heavy sections like forging of thick plate. This is the reason why plane strain fracture toughness is used in thick sectional structural member in aerospace applications.

    TABLE 2 COMPARISON OF ANALYTICAL AND EXPERIMENTAL FRACTURE STRENGTH OF M300 GRADE MARAGING STEEL SCT SPECIMENS (t=3mm, ult= 2255MPa, KF=151.7 MPa, m=0.4, p=15.8)

    Width (mm)

    Crack Dimensions (mm)

    Fracture strength f (MPa)

    W

    A

    2c

    Test

    Analysis

    Relative Error (%)

    15.2

    0.8

    4.0

    2008.0

    1879.8

    6.4

    15.2

    1.1

    5.0

    1668.5

    1705.7

    -2.2

    15.1

    1.1

    5.8

    1566.8

    1646.4

    -5.1

    19.6

    1.4

    7.5

    1426.9

    1446.8

    -1.4

    18.4

    1.4

    7.2

    1367.9

    1458.8

    -6.7

    19.1

    1.7

    9.0

    1349.1

    1259.7

    6.6

    18.5

    1.7

    7.5

    1220.0

    1349.1

    -10.6

    Stantard error obtained is 0.063

    TABLE 3 COMPARISON OF ANALYTICAL AND EXPERIMENTAL FRACTURE STRENGTH OF M300 GRADE MARAGING STEEL CYLINDRICAL VESSELS HAVING SURFACE CRACKS.

    (D0= 77.2mm, t=3mm, ys= 2120 MPa, ult = 2255MPa, KF=148.6 MPa, m=0.4, p=15.8)

    Crack Dimensions (mm)

    Failure pressure Pbf (MPa)

    a

    2c

    Test

    Analys is

    Relative error (%)

    0.4

    2.5

    193.8

    174.6

    9.9

    0.9

    4.0

    157.7

    157.2

    0.3

    1.0

    5.5

    158.6

    145.9

    8.0

    1.4

    5.2

    144.0

    139.8

    3.0

    1.6

    10.0

    105.7

    105.5

    0.2

    1.7

    12.0

    99.0

    96.6

    2.5

    1.7

    8.0

    117.7

    112.7

    4.3

    1.8

    14.0

    94.3

    85.3

    9.5

    Stantard error obtained is 0.06

    TABLE 4 COMPARISON OF ANALYTICAL AND EXPERIMENTAL FRACTURE STRENGTH OF M250 GRADE MARAGING STEEL PARENT METAL SCT SPECIMENS

    (W=15mm, t= 7.5mm, ult=1860MPa, KF == 235.7 MPa, m=0.6, p=20.4)

    Crack dimensions(mm)

    Fracture strength, f (MPa)

    a

    2c

    Test

    Analysis

    Relative error (%)

    1.3

    2.7

    1850

    1746.4

    5.6

    1.4

    3.0

    1850

    1737.0

    6.1

    1.5

    3.4

    1840

    1719.3

    6.6

    1.7

    3.8

    1831

    1702.1

    7.0

    1.7

    4.1

    1820

    1689.5

    7.2

    1.7

    4.3

    1830

    1681.3

    8.1

    1.8

    4.0

    1822

    1692.9

    7.1

    2.0

    4.0

    1830

    1691.9

    7.5

    1.9

    4.8

    1798

    1656.1

    7.9

    2.0

    4.9

    1800

    1651.8

    8.2

    2.0

    4.5

    1786

    1668.3

    6.6

    2.0

    4.4

    1802

    1673.0

    7.2

    2.2

    4.8

    1783

    1651.1

    7.4

    2.0

    5.0

    1788

    1644.8

    8.0

    2.2

    5.3

    1771

    1625.5/p>

    8.2

    2.2

    5.7

    1760

    1605.2

    8.8

    2.3

    5.9

    1760

    1591.5

    9.6

    2.5

    5.8

    1754

    1590.7

    9.3

    2.5

    6.3

    1711

    1562.5

    8.7

    2.5

    6.5

    1730

    1551.5

    10.3

    1.6

    3.9

    1796

    1698.8

    5.4

    1.7

    4.2

    1825

    1685.4

    7.7

    2.0

    4.7

    1817

    1658.9

    8.7

    2.1

    5.1

    1753

    1637.8

    6.6

    2.1

    5.2

    1772

    1632.9

    7.9

    2.5

    6.3

    1732

    1562.5

    9.8

    2.5

    6.8

    1713

    1535.1

    10.4

    Stantard error obtained is 0.079

    TABLE 5: COMPARISON OF ANALYTICAL AND EXPERIMENTAL FRACTURE STRENGTH OF M250 GRADE MARAGING STEEL PARENT METAL SCT SPECIMENS

    (W=15mm, t= 7.5mm, ult=1720MPa, KF =235.7 MPa, m=0.6, p=20.4)

    Crack dimensions(mm)

    Fracture strength (MPa) f

    a

    2c

    Test

    Analysis

    Relative error (%)

    1.3

    2.7

    1735

    1627.0

    6.2

    1.5

    2.7

    1713

    1620.0

    5.4

    1.0

    2.8

    1700

    1625.4

    4.4

    1.1

    2.8

    1752

    1624.5

    7.3

    1.7

    3.8

    1711

    1592.9

    6.9

    1.5

    3.9

    1706

    1591.5

    6.7

    1.4

    3.9

    1700

    1592.9

    6.3

    1.5

    4.0

    1736

    1588.7

    8.5

    1.6

    4.8

    1711

    1564.6

    8.6

    2.2

    5.0

    1666

    1546.8

    7.2

    2.0

    5.0

    1682

    1549.8

    7.9

    2.0

    5.3

    1621

    1539.3

    5.0

    2.2

    5.4

    1654

    1531.4

    7.4

    1.9

    5.7

    1616

    1528.8

    5.4

    2.3

    6.0

    1581

    1506.5

    4.7

    2.7

    6.2

    1590

    1485.6

    6.6

    2.2

    6.6

    1590

    1485.5

    6.6

    2.2

    6.8

    1553

    1478.0

    4.8

    Stantard error obtained is 0.066

    TABLE 6: COMPARISON OF ANALYTICAL AND EXPERIMENTAL FRACTURE STRENGTH OF M250 GRADE MARAGING STEEL PARENT METAL SCT SPECIMENS

    (W=15mm, t= 7.5mm, ult=1720MPa, KF == 235.7 MPa, m=0.6, p=20.4)

    Crack dimensions(mm)

    Fracture strength, f (MPa)

    a

    2c

    Test

    Analysis

    Relative error (%)

    1.0

    2.7

    1703

    1628.6

    4.4

    1.2

    2.9

    1732

    1621.8

    6.4

    1.9

    4.0

    1724

    1587.5

    7.9

    1.9

    4.2

    1689

    1581.0

    6.4

    1.9

    4.2

    1726

    1581.0

    8.4

    1.8

    4.3

    1721

    1578.5

    8.3

    2.1

    4.9

    1703

    1556.4

    8.6

    2.2

    5.0

    1690

    1551.9

    8.2

    2.2

    5.2

    1662

    1544.9

    7.0

    2.2

    5.2

    1713

    1544.9

    9.8

    2.5

    5.6

    1668

    1526.4

    8.5

    2.3

    5.9

    1693

    1518.9

    10.3

    2.8

    6.0

    1647

    1506.1

    8.6

    Stantard error obtained is 0.080

  4. FAILURE ASSESSMENT DIAGRAM (FAD)

    Failure assessment diagram is widely employed to ensure the safety of defected engineering or structural components. FAD helps to address the acceptable and unacceptable range of a material. FAD for Table 2 and 4 are given below.

    Fig.2. FAD for Table 1

    For both figures Kmax is plotted along horizontal axis and f/ult ratio along vertical axis. Dark line represents curve for specimens given in tables. Dotted line represents the smoothened fitted curve. The area within the curve is the acceptable region and the area outside the curve is the unacceptable region for the concerned material. For figure 1, f/ult is maximum when Kmax is 20%. The maximum value of f/ult is 0.920. Similarly in the case of figure 2, the maximum value of f/ult is 0.880. For both the cases

    f/ult is minimum when Kmax is 100%.

    Fig.3. FAD for Table 3

  5. CONCLUSION

Fracture strength of M250 and M300 grade maraging steel parent SCT specimens has been evaluated analytically using MATLAB coding and compared with the available test datas and computed relative error for each specimen considered. Failure assessment diagram for one specimen of M250 and M300 grade maraging steel has been drawn and determined the area of acceptance.

REFERENCES

  1. B.Nageswara Rao and A.R Acharya, J.D.A Subramanyam, N.R.U.K KarthaBurst pressure estimation of a maraging steel chamber with surface cracks, International Journal For Fracture Mechanics (in press)

  2. Margetson J (1978) Burst pressure prediction of rocket motors, AIAA Paper no.78-1569

  3. T. Christopher, B S V Rama Sarma, P.K.G Potti, B N Rao and K.Sankaranarayanaswamy (2002) Assessing the failure of cylindrical pressure vessels due to longitudinal weld misalignment ,International Journal Of pressure vessels and piping Volume No.79

  4. K.M Rajan, P.U Deshpande, K.Narasimhan, Experimental studies on burst pressure of thin walled flow formed pressure vessels,

    International Journal of materials and processing technology

  5. Nidhi Dwivedi, Veerendra Kumar (2012) Burst pressure estimation of pressure vessels

using FEA International Journal Of Engineering Research And Technology (IJERT), Vol. 1, Issue 7, September.

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