DOI : 10.17577/IJERTCONV3IS29038
- Open Access
- Total Downloads : 6
- Authors : Sreedevi Lekshmi, Anup Joy
- Paper ID : IJERTCONV3IS29038
- Volume & Issue : NCRACE – 2015 (Volume 3 – Issue 29)
- Published (First Online): 30-07-2018
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
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.
-
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.
-
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 2f 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
-
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
-
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
-
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
-
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)
-
Margetson J (1978) Burst pressure prediction of rocket motors, AIAA Paper no.78-1569
-
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
-
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
-
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.