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An analysis of the specific heat loss at the tip of severely notched stainless steel specimens to correlate the fatigue strength
Accepted Manuscript An analysis of the specific heat loss at the tip of severely notched stainless steel specimens to correlate the fatigue strength D. Rigon, M. Ricotta, G. Meneghetti PII: DOI: Reference:
S0167-8442(17)30294-X http://dx.doi.org/10.1016/j.tafmec.2017.09.003 TAFMEC 1946
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
4 June 2017 21 August 2017 1 September 2017
Please cite this article as: D. Rigon, M. Ricotta, G. Meneghetti, An analysis of the specific heat loss at the tip of severely notched stainless steel specimens to correlate the fatigue strength, Theoretical and Applied Fracture Mechanics (2017), doi: http://dx.doi.org/10.1016/j.tafmec.2017.09.003
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AN ANALYSIS OF THE SPECIFIC HEAT LOSS AT THE TIP OF SEVERELY NOTCHED STAINLESS STEEL SPECIMENS TO CORRELATE THE FATIGUE STRENGTH D. Rigon, M. Ricotta, G. Meneghetti* University of Padova, Department of Industrial Engineering, via Venezia, 1, 35131 Padova (Italy)
*Corresponding author: [email protected]
ABSTRACT The specific heat loss per cycle (Q parameter) was used in previous works to synthesize more than one hundred experimental fatigue test results generated from plain and bluntly notched specimens made of AISI 304L stainless steel. It was shown that Q can be estimated at a point of a specimen or a component starting from the cooling gradient measured immediately after the fatigue test has been stopped. Since the cooling gradient was measured by means of thermocouple wires attached to the specimen’s surface by means of a 1.5-to-2 mm glue dot diameter, notches with tip radii greater than 3 mm were tested, because the glue dot diameter would have been too large to capture the specific heat loss at the tip of sharper notches. In this paper, the cooling gradient has been measured by means of an infrared camera, equipped with proper lens and an extender ring to achieve a 20 m/pixel spatial resolution; therefore the investigation could be extended for the first time to notch tip radii lower than 3 mm. Fully reversed axial fatigue tests have been carried out on 4-mm-thick, hot-rolled AISI 304L stainless steel specimens. As a result, the new fatigue data have been found to collapse inside the existing heat energy -based scatter band previously calibrated on blunter notches. The heat energy distribution close to the notch tip has also been investigated.
Keywords: energy dissipation, energy methods, AISI 304L, fatigue, notch effect, energy distribution
INTRODUCTION
A material subjected to cyclic loads dissipates energy, which causes an increase of the temperature. In constant amplitude fatigue tests characterized by a given stress amplitude, mean stress and stress state, the temperature of the specimen’s surface reaches a stable value that depends on the load test frequency, the specimen’s geometry and the temperature of the surroundings. Starting from this experimental evidence, some methods were developed to estimate rapidly the fatigue limit in metallic materials and components [1-5], to detect the initiation and propagation of damage in metal materials as well as in composites [6-9] and to analyse the fatigue behaviour under constant amplitude [10-12] as well as block loading [13-15]. Since the equilibrium temperature achieved during a fatigue test depends on the thermal and mechanical boundary conditions, the specific heat energy per cycle, Q, was assumed as a fatigue damage indicator [16], because it is expected to be a material property, similarly to the plastic strain hysteresis energy [17]. In [16] a theoretical model and an experimental procedure were proposed to evaluate the Q parameter, taking advantage of temperature measurements, which can be performed by using an infrared camera. In the present paper, the temperature field was measured both on the specimen’s surface (frontal view) and in the thickness (lateral view), as illustrated in Figure 1a. The reason for that will be explained later on. At the beginning of a fatigue test, the material temperature T(t) increases and then stabilises at a value,
Tst , when the thermal equilibrium is achieved between the thermal power “generated” by the material and that dissipated to the surroundings, as shown in Figure 1b. The alternating component superimposed to Tm ( t ) is due to the thermoelastic effect. By applying the energy balance equation to a control volume V of a material undergoing a fatigue test (see Figure 2), the first law of thermodynamics applied over one loading cycle can be written as [16]:
W dV Q U dV V
(1)
V
W being the input mechanical energy per cycle (the area within the hysteresis loop), Q the dissipated thermal energy and U the variation of internal energy. Eq 1 can be written by considering the mean power exchanged over one loading cycle:
ij dij f L dV H dV c
V
V
V
Tm t E p dV t
(2)
where fL is load test frequency, H=QfL is the thermal power dissipated by conduction, convection and radiation, the material density, c the specific heat and E p the rate of accumulation of damaging energy in a unit volume of material. Since Eq. (2) considers the rate of energy contributions averaged over one cycle, thermoelasticity does not produce a net energy dissipation or absorption, because it consists of a reversible exchange between mechanical and thermal energy over one loading cycle. Therefore, the mean temperature evolution Tm ( t ) appears on the right side of Eq. 2. When temperature stabilises (t > ts in Figure 1b), the first derivative of Tm ( t ) becomes null, therefore Eq.2 simplifies to:
ij dij f L dV H dV E p dV V
V
(3)
V
If referred to a point on the specimen’s surface, Eq. 3 becomes
W fL H E p
(4)
Suppose now to stop suddenly the fatigue test at t=t* (see Figure 1b): then just after t* (i.e. at t=t*+)
the mechanical input power W f L and the rate of accumulation of fatigue damage E p will vanish. By writing the energy balance equation (2) again, we obtain:
c
T( t ) H t t ( t*)
(5)
It is worth noting that the thermal power H dissipated to the surroundings just before and just after t* is the same in Eq. (4) and in Eq. (5), respectively, because the temperature field is continuous through t*. Finally, the thermal energy released in a unit volume of material per cycle can be calculated by simply accounting for the load test frequency, fL:
c Q
H fL
T( t ) t t ( t*)
(6)
fL
Equation (6) enables one to measure readily and in-situ the specific heat loss Q at any point of a specimen or a component undergoing fatigue loadings. The Q parameter was adopted to synthesise 140 experimental results obtained from constant amplitude, push-pull, stress- or strain-controlled fatigue tests carried out on plain and notched hot rolled AISI 304L stainless steel specimens [18-20] as well as from cold drawn un-notched bars of the same steel, under fully-reversed axial or torsional fatigue loadings [21]. Later on, the mean stress influence in fatigue has also been taken into account [22]. The fatigue test results synthesised in term of Q are reported in Figure 3: all of them fall in a single energy-based scatter band, which was originally fitted only on the fatigue test results relevant to plain material, hole specimens, U and bluntly V-notched specimens [19]. Since in refs [18-20] the cooling gradients were measured by
means of thermocouple wires attached to the specimen’s surface by means of a 1.5-to-2 mm glue dot diameter, notches with tip radii greater than 3 mm were tested ,because the glue dot diameter would have been too large to capture the specific heat loss at the tip of sharper notches. In this paper, the use of the specific energy Q has been extended to more severe notches, taking advantage of the much improved spatial resolution provided by the adopted infrared camera. Therefore, specimens characterized by 3, 1 and 0.5 mm notch tip radii have been tested. As a result, the new fatigue data were seen to collapse inside the existing heat energy-based scatter band previously calibrated. Finally, the energy distribution around the notch tip Q(x,y) was investigated and it was found that the gradient of Q(x,y) tends to level off while approaching the notch tip.
MATERIAL AND TEST METHOD
Constant amplitude, completely reversed, stress-controlled fatigue tests were carried out on 4-mm thick, hot rolled AISI 304L stainless steel specimens, having notch tip radii r n equal to 3, 1, and 0.5 mm, as reported in Figure 4a. The mechanical properties and the chemical composition are reported in Table 1 [20], while Figure 4b shows the austenitic microstructure of the material. The analysed stainless steel had a material density and the specific heat c equal to 7940 kg/m3 and 507 J/(kg K), respectively [15,23]. Starting from 46 x 150 mm rectangular plates, notches were obtained by wire electro discharge machining, followed by electrochemical polishing. After that, the specimen surfaces were polished using progressively finer emery papers (until the maximum paper grade of 4000 was reached), in order to prepare the surface for fatigue crack monitoring. One surface of the specimen as well as the notch root in the thickness direction were black painted to increase the material emissivity in view of the infrared thermal acquisitions, as will be discussed in the next sections.
The net-section stress concentration factors, Ktn, were evaluated by carrying out 3D linear elastic finite element analyses and resulted 3.41, 4.85 and 6.10, for r n equal to 3, 1 and 0.5 mm, respectively. To take into account the machine grip effect, displacements were applied to the relevant lines shown in Figure 4a. The fatigue tests were carried out by using a servo-hydraulic Schenck Hydropuls PSA 100 machine having a 100 kN load cell and equipped with a TRIO Sistemi RT3 digital controller. Load test frequencies were set in the range between 3 and 40 Hz, depending on the applied stress level, in order to keep the material temperature below 60 °C. A total number of 25 specimens was fatigue tested,and the number of cycles to failure, Nf, was equal to that for complete separation. The temperature field T(x,y) close to the notch apex (see the “frontal view in Figure 1a) was measured by using a FLIR SC7600 infrared camera, operating at a frame rate, facq, equal to 200 Hz, having a 1.5-5.1 m spectral response range, 50 mm focal lens, a noise equivalent temperature difference (NETD) < 25 mK and an overall accuracy of 0.05°C. It was equipped with an analog input interface, which was used to synchronize the force signal coming from the load cell with the temperature signal. Furthermore, a 30-mm-long extender ring was adopted to achieve a spatial resolution of approximately 20 m/pixel. Due to the presence of the extender ring, the Field of View (FoV) was reduced to 320x256 pixels. To avoid vignetting, the temperature field around the notch tip was acquired by positioning the notch tip itself in the centre of the Field of View (FOV). Infrared images were analyzed by means of the ALTAIR 5.90.002 commercial software. To monitor the evolution of Q during each test, 1 to 10 cooling gradients (depending on the applied stress levels) were performed using a 10-second-long sampling window, translating into 2000 acquired frames, the frame rate being facq=200 Hz. More precisely, acquisitions consisted of approximately 5 seconds of running test (1000 frames between t s and t* in Figure 1b) followed by the machine stop at the time t*, and the remaining 5 seconds, during which the cooling gradient was captured and additional 1000 frames were acquired . The machine test was stopped by using a manual trigger signal. The span rate of the test machine was set to 100% to induce a test stop as
abrupt as possible. Qualitatively, it took approximately two tapered force cycles to reach a complete stop as depicted in Figure 11, which will be commented in the next paragraph. After the test stop, the set point of the machine was kept to the zero load level during the cooling phase. The crack length was measured by means of a AM4115ZT Dino-lite digital microscope operating with a magnification ranging from 20x to 220x. The microscope and the infrared camera monitored the opposite surfaces of the specimens, as shown in Figure 5.
FATIGUE TEST RESULTS AND ENERGY-BASED ANALYSIS
All fatigue test results, presented elsewhere by the authors [24], are summarised in Figure 6 in terms of net-section stress amplitude, an. The 10%-90% Survival Probability (PS) scatter band reported in the figure was originally calibrated in [19], by considering fatigue test results carried out on Uand V-notched (2 = 90°, see Figure 1a) specimens with tip radii equal to 5 mm and 3 mm, respectively, and assuming a log-normal distribution of the number of cycles to failure with a 95% confidence level. The mean curve, the inverse slope k, the stress-based scatter index T (an10%/an90%) and the life-based index TN, (TN,Tk) are also reported. It can be seen that the new experimental results fall inside the previously defined scatter band. However, plain specimens exhibit higher fatigue strength, as reported in Figure 6. To illustrate the evolution of the surface temperature, long-term acquisitions were performed for three specimens, equipped with copper-constantan thermocouple wires having diameter 0.127 mm, which were fixed at a distance of 5 mm above the notch tip (see Figure 7), by means of a silver loaded conductive epoxy glue. A low sample rate of 2 Hz was adopted by using a Agilent HP 34970A data logger. Results reported in Figure 7 are just exemplary data, which were not processed further. It is worth noting that in this figure the thermoelastic effect could not be measured, because
the sample rate adopted to acquire the temperature signal was too low as compared to the frequency of the thermoelastic temperature, which obviously coincided with the load test frequency fL. Figure 7 shows that several stops were done during a single fatigue test, until a fatigue crack emanating from the notch tip was detected by the digital microscope. The first crack detected in the case of specimens V_135_R3_07 and V_135_R3_08 are shown in Figure 8. After detecting a crack for the first time, having length “a“ at a number of cycles N* reported in Figure 7, the fatigue test was run to final failure without further stops and cooling gradient measurements. Figure 7 shows that temperature was not stabilised before the test stop, as opposed to the situation illustrated in previous Figure 1b. Therefore, the internal energy term associated to the time derivative of Tm(t) on the right hand side of Eq. (2) is different from zero. As a conclusion, Equations from 3 to 6 should not be applied, strictly speaking, because they assume that the time derivative of T m(t) is zero. However, by considering as an example the test stop highlighted in Figure 7 and the relevant temperature acquisitions reported in the next Figure 10a, it could be verified that the cooling gradient just after t* is 24 times higher than the heating gradient (i.e. dTm/dt) just before t*. Therefore, of the total heat production, the dissipated fraction is by far greater than the self-heating fraction. Given that, Equations 3 to 6 were considered to be applicable in an engineering sense. During each fatigue test several test stops were performed before N* to monitor the evolution of the energy parameter Q, according to Eq (6). Typical examples of temperature maps captured at the notch tips at time t=t* (see Figure 1b) are shown in Figure 9, for different notch radii and applied nominal stress amplitude, an. Figure 9 highlights that the maximum temperature was achieved in the case of the highest stress amplitude and the greatest notch radius (Figure 9a), where heat generation involves a certain volume of material embracing the notch tip. In this case, the load test frequency was set sufficiently low to limit the maximum material temperature below 60 °C, as mentioned above. Figure 10a-f shows the temperature versus time acquisitions relevant to Figure 9a-f, respectively. In particular, Figure 10 reports the maximum temperature Tmax extracted frame-
by-frame from a circular area embracing the notch, as shown in the detail of Figure 4a: essentially Tmax is the temperature at the notch tip. It can be seen that for the notch tip radii analysed, the time window considered to calculate the cooling gradient is of the order of one tenth of a second and the corresponding temperature decrease is of the order of some tenths of a degree. In Figure 10a-f it can be observed that the test machine takes some tenths of a second to completely stop cycling. As a consequence, the force as well as the associated thermoelastic signals reduce in a tapered way, as illustrated in Figure 11. Therefore an operational definition of the time t* was adopted, when the test machine was assumed to stop cycling and the cooling gradient was measured. Such a definition was as follows: t* is the time (after triggering the machine stop) when the first force peak is within a range of ±2.7 kN. In all experimental situations analysed in the present work, it was verified that the first peak within the range ±2.7 kN was below 5% of the force amplitude applied during the relevant fatigue test. The evolution of heat energy Q versus the fatigue life normalised with respect to Nf is reported in Figure 12, which highlights a range of values from 0.28 to 1.73 MJ/(m3cycle), that means a factor of 6.18. In view of this body of evidence, the Q parameter can be assumed reasonable constant during a single fatigue test, as compared to the wide range of energy levels measured for the different applied net-stress amplitudes. Therefore, the fatigue tests results were reanalysed in terms of average Q, taken from Figure 12. Figure 13 shows that the new fatigue data fall inside the existing heat energy -based scatter band previously calibrated on blunter notches [19]. Plain material data fall in the same scatter band, as opposed to previous Figure 6.
HEAT ENERGY DISTRIBUTION CLOSE TO THE NOTCH TIP
Additional analyses were performed to investigate the energy distribution close to the notch tip, because this topic might be of interest in view of applying the proposed approach to pointed V-
notches, including crack propagation analyses. Investigations in this direction have been performed recently [20,24,25], because it is well known that stress-/strain- or strain energy density-based approaches take into account the distributions (and not just peak values) of the adopted fatiguerelevant parameter. Having measured the temperature maps close to the notch tip, as reported in previous Figure 9, the distribution of the energy parameter Q(x,y) could be calculated taking advantage of a numerical procedure developed in Matlab® environment, which calculated pixel-by-pixel the cooling gradient according to Eq. 6. After some preliminary analyses, for the sake of simplicity the time-window adopted to evaluate the cooling gradient was chosen equal to 0.1s and it was kept constant for all pixels processed. Figure 14a shows as an example the energy distribution Q(x,y) measured at N=8.12·103 cycles in the case of a specimen having r n=0.5 mm, a=130 MPa and Nf =6.76·104 cycles, while Figure 14b shows the distribution Q(x,0) along the notch bisector, starting from the notch tip (x=0). Figure 14a shows that the specimen edge is not well defined due to the well-known edge effect characteristic in thermography (see [26] as an example). Therefore, the picture taken with the digital microscope on the opposite side of the specimen was used to single-out the notch tip location and to transfer it at the co-ordinates (x=0, y=0) reported in Figure 14a. A gentle scratch made on both surfaces of the specimens at the same distance from the free edge made transferability possible. After positioning the notch tip at (x=0, y=0), the negative portion of the picture (x<0) was removed, as it will be seen in the next Figures 15 and 17. Figures 14a and 14b show that a certain level of noise exists; therefore, in order to smooth the energy fields, raw data shown in Figure 14 were filtered by applying the “imgaussfilt” function available in Matlab® code, so that a much smoother heat distribution Q flt(x,y) was obtained. Figure 15 reports the result obtained after processing the data reported in Figure 14 and shows that the gradient of the thermal energy tends to decrease while approaching the notch tip, where the maximum energy dissipation Q0=Q(0,0) exists.
To support the peak thermal energy just evaluated at the notch tip, during the fatigue test carried out on the specimen to which Figure 14 is referred to, thermal maps were taken both from the frontal and from the lateral views (see Figure 1a). More precisely, after a given test stop to acquire the cooling phase from the frontal view, the specimen was turned 90° and the test was restarted, followed shortly after by a new stop to acquire the cooling gradient from the lateral view. Figure 16a shows the temperature distribution at the notch tip taken from the lateral view and Figure 16b shows the Q values measured at different locations along the specimen thickness, resulting in a mean value Q=0.55 MJ/(m3cycle). Such a value has been reported at x=0 in Figure 15b and it is seen in excellent agreement with the value calculated at the notch tip from the energy distribution measured at the specimen surface. Figure 15a reports also the constant-Q contours; in particular, a circular contour is plotted, which identifies the biggest region where the dissipated energy is equal to or higher than 90% the maximum energy calculated at the notch tip, Q0. In figure 15a the size of such circular region is RQ,90%=0.54 mm. Figure 17 reports the energy distributions Q(x,y) as well as the distributions along the notch bisector Q(x,0) for other specimens characterised by different notch radii and applied stress amplitudes. A selection of results is also summarised in Table 2 and it is seen that RQ,90% ranges from 0.53 to 0.87 mm. In a previous work, the structural volume size for fatigue strength estimations was evaluated for the same material and test conditions and it resulted equal to 0.52 mm [25]. Living aside the definition of the structural volume and the description of the fatigue strength criterion, which are out of the scope of the present paper, the results found here support the conclusion that the energy dissipation for the present material, notch geometries and testing conditions is reasonably constant inside the structural volume.
CONCLUSIONS
In order to extend the heat energy-based approach to more severely notched specimens as compared to those tested previously, constant amplitude, completely reversed, stress-controlled fatigue tests have been carried out on hot rolled, 4-mm-thick notched specimens made of AISI 304L stainless steel specimens having notch tip radii equal to 3, 1, and 0.5 mm. The specific heat energy Q was evaluated at the notch tip by means of an infrared camera with a spatial resolution equal to 20 m/pixel. Several evaluations were performed during a fatigue test, until the initiation of a crack was detected by means of a digital microscope. As a result, the specific heat loss Q was seen to be approximately constant during individual fatigue tests. This outcome has an important practical consequence, in that fatigue life can be anticipated starting from measurement performed at the beginning of the fatigue test. If presented in terms of specific heat energy at the notch tip versus the number of fatigue cycles to failure, the new experimental data were seen to fall inside the energy-based scatter band calibrated previously by the authors on fatigue data obtained on plain as well as notched specimens, characterised by larger notch tip radii than those tested in the present contribution. Finally, the heat energy distribution close to the notch tip was also investigated by estimating the size of the region near the notch tip where energy dissipation is equal to or greater than 90% the maximum value existing at the notch apex. Such region was assumed to be circular and centered at the notch tip. It was found that for the analysed material, notch geometries and testing conditions, its radius is equal to some tenths of a millimetre.
ACKNOWLEDGEMENTS This work was carried out as a part of the project CODE CPDA145872 of the University of Padova. The Authors would like to express their gratitude for financial support.
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AN ANALYSIS OF THE SPECIFIC HEAT LOSS AT THE TIP OF SEVERELY NOTCHED STAINLESS STEEL SPECIMENS TO CORRELATE THE FATIGUE STRENGTH D. Rigon, M. Ricotta, G. Meneghetti* University of Padova, Department of Industrial Engineering, via Venezia, 1, 35131 Padova (Italy)
*Corresponding author: [email protected]
CAPTIONS TO TABLES AND FIGURES Table 1: Mechanical properties and chemical composition of the hot-rolled AISI 304L stainless steel. Table 2: Value of radius RQ,90% measured during the fatigue test.
Figure 1. Experimental set-up adopted (a) and evaluation of the cooling gradient (from Eq. (1)) during a fatigue test (b) Figure 2. Energy balance of a material subjected to cyclic loading. Figure 3. Fatigue tests results in terms of specific heat energy. The scatter band was calibrated only on data published in [19]. Figure 4. Specimen geometry (thickness is 4mm, 2=135°) (a) and AISI 304L austenitic microstructure (b). Figure 5. Test setup consisting of a FLIR SC7600 infrared camera, a AM4115ZT Dino-lite digital microscope and the specimen clamped in the test machine. Figure 6. Fatigue data analysed in terms of net-section stress amplitude. Scatter band was calibrated in [19]. Figure 7. Typical temperature evolution measured at a distance of 5 mm from the notch apex by using thermocouples. Figure 8. Crack inspection by using the digital microscope for two of the fatigue tests reported in Figure 7 characterised by an = 190 MPa, N* = 3.20·103 cycles (a) and an = 180 MPa, N* = 7.86•103 cycles (b). Figure 9. Temperature maps observed during the fatigue tests. Figure 10. Typical cooling gradients at the notch tip measured during the fatigue tests. Figure 11. Definition of the time t* when the machine is assumed to stop cycling and the cooling gradient is evaluated. Figure 12. Specific heat loss measured during the fatigue tests. Figure 13. Fatigue data reported in figure 6 analysed in terms of specific heat loss per cycle. Scatter band is defined for 10% and 90% survival probabilities and it is taken from [19].
Figure 14. Heat energy distribution Q(x,y) measured close to the notch tip (a) and along the notch bisector (y=0) (b) for a specimen characterized by rn=0.5 mm, an=130 MPa, N*=1.48·104 and Nf=6.76·104. Picture was taken at N=8.12·103 cycles. Figure 15. Heat energy distribution Qflt(x,y) from Figure 14a after data filtering (a) and the relevant distribution evaluated along the notch bisector (y=0) (b). Figure 16. Temperature distribution measured along the notch tip from the lateral view (see Figure 1) (a) and the corresponding energy distribution (b). Figure 17. Heat energy distributions at the notch tip: (a,b,) rn=3 mm, an=170 MPa, Nf=1.85·104; (c,d) rn=1 mm, an=150 MPa, Nf=1.67·104, (e,f) rn=0.5 mm, an=100 MPa, Nf=1.35·105.
Table 1: Mechanical properties and chemical composition of the hot-rolled AISI 304L stainless steel. Rp0.2%
Rm
A
A,-1,50%
(MPa)
(MPa)
(%)
(MPa)
279
620
57
202
HB
170
C
Mn
Si
Cr
Ni
P
S
N
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
0.026
1.470
0.370
18.1
8.2
0.034
0.001
0.058
Table 2: Value of radius RQ,90% measured during the fatigue test. rn
an
fL
Nf
N*/Nf
Q0
RQ,90% 3
[mm]
[MPa]
[Hz]
3
190
10
7.82·103
3
170
10
3
110
1
N/Nf
[MJ/(m cycle)]
[mm]
0.41
1.98
0.85
0.24
1.85·104
0.61
1.45
0.87
0.42
25
2.71·105
0.67
0.38
0.55
0.17
150
10
1.67·104
0.33
1.17
0.64
0.28
1
120
15
7.68·104
0.40
0.42
0.55
0.13
0.5
190
5
8.17·103
0.40
1.77
0.83
0.21
0.5
100
35
1.35·105
0.13
0.51
0.53
0.08
0.5
130
25
6.76·104
0.22
0.55
0.54
0.12
a)
b)
F(t) T(x,y;t)
T(t) Tmax infrared camera (frontal view)
y 2 Tst
x
t
Tm(t)
infrared camera (lateral view)
ts
t*
t t
t
Figure 1. Experimental set-up adopted (a) and evaluation of the cooling gradient (from Eq. (1)) during a fatigue test (b)
F(t) W
V
n
U
Q
Figure 2. Energy balance of a material subjected to cyclic loading.
100 Scatter band: 10-90% survival probabilities, from [19] k=2.11, TQ=2.04, TN=4.50 QA,50%=0.133 MJ/(m3 cycle) R=-1
Q [MJ/(m3 cycle)]
10
Data from [21] Axial load Torsional load Data from [20] Plain material rn =3mm V-notch rn =1mm 2=90 rn =0.5mm
k 1
AISI 304L 1
0.1
Data from [19] Plain specimens Stair-case: broken, unbroken Hole, rn =8mm U-notch, rn =5mm Blunt V-notch, 2=90 , rn =3mm + Strain controlled
0.01 1.E+2
1.E+3
≈ 140 test results
1.E+4 1.E+5 1.E+6 Nf, number of cycles to failure
1.E+7
1.E+8
Figure 3. Fatigue tests results in terms of specific heat energy. The scatter band was calibrated only on data published in [19]. a)
b) Machine grip
Area from which Tmax was extracted
rn rn 2
150 90
8 50 m
46
Machine grip
Figure 4. Specimen geometry (thickness is 4mm, 2=135°) (a) and AISI 304L austenitic microstructure (b).
Digital microscope
Infrared camera
Figure 5. Test setup consisting of a FLIR SC7600 infrared camera, a AM4115ZT Dino-lite digital microscope and the specimen clamped in the test machine.
500 plain material from [20], k=17.2 A, 1,50%= 202 MPa
an [MPa]
1 100
k
AISI 304L R=-1 Scatter band: 10-90% survival probabilities, from [19] k=5.8, T=1.30, TN=4.60 Present work rn =3 mm, Ktn = 3.41 rn =1 mm, Ktn = 4.85 rn =0.5 mm, Ktn = 6.10 10 1.E+3
1.E+4
Short stair-case unbroken, broken
V-notch 2=135
1.E+5 1.E+6 Nf, number of cycles to failure
1.E+7
1.E+8
Figure 6. Fatigue data analysed in terms of net-section stress amplitude. Scatter band was calibrated in [19].
100 90
N* (a = 0.17 mm)
80
N* (a = 0.25 mm)
70
a
Test stop (see Figure 10a)
60 T [ C]
thermocouple
N* (a = 0.13 mm)
5 m m
50 40
30 V_135_R3_07 an = 190 MPa, fL= 5 10 Hz V_135_R3_08 an = 180 MPa, fL= 10 Hz V_135_R3_06 an = 170 MPa, fL= 10 Hz
20 10 0 0
5000
10000 N, number of cycles
15000
20000
Figure 7. Typical temperature evolution measured at a distance of 5 mm from the notch apex by using thermocouples.
a)
b)
Crack tip
Crack tip 200 m
200 m
Figure 8. Crack inspection by using the digital microscope for two of the fatigue tests reported in Figure 7 characterised by an = 190 MPa, N* = 3.20·103 cycles (a) and an = 180 MPa, N* = 7.86·103 cycles (b).
rna)= 3 mm, an = 190 MPa, fL = 10 Hz
b) rn = 3 mm, an = 110 MPa, fL = 25 Hz
500 m
c) rn = 1 mm, an = 150 MPa, fL = 10 Hz
500 m
d) rn = 1 mm, an = 120 MPa, fL = 15 Hz
500 m
500 m
rn = 0.5 mm, an = 190 MPa, fL = 5 Hz e)
f) rn = 0.5 mm, an = 100 MPa, fL = 35 Hz
500 m
Figure 9. Temperature maps observed during the fatigue tests.
500 m
53 52.5 52
Tmax [ C]
b) 42
an = 190 MPa Nf = 7.82·103 cycles fL = 10 Hz t t t
51.5
= 0.20 °C/s
51 50.5
t t t
= -4.81 °C/s
50
41
t t t
= -2.02 °C/s
40.5 rn = 3 mm
49.5
rn = 3 mm
49
40 -0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
c) 40.5
1
t t t
33.8
39
38.5 38
= -1.67 °C/s
t t t
33.4
33.2 33
rn = 1 mm
1
an = 120 MPa Nf = 7.68 ·104 cycles fL = 15 Hz
33.6
= -2.80 °C/s
Tmax [ C]
39.5
-0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s] d) 34
an = 150 MPa Nf = 1.67·104 cycles fL = 10 Hz
40 Tmax [ C]
an = 110 MPa Nf = 2.71·105 cycles fL = 25 Hz
41.5 Tmax [ C]
a)
rn = 1 mm
32.8 -0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
e) 39.5
1 f) 38.5
an = 190 MPa Nf = 8.17·103 cycles fL = 5 Hz
39
-0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
38
1
an = 100 MPa Nf = 1.35·105 cycles fL = 35 Hz
t t t
= -1.75 °C/s
Tmax [ C]
Tmax [ C]
37.5 38.5 38
37.5
37
37
= -4.11 °C/s
36.5 36
rn = 0.5 mm
t t t
rn = 0.5 mm
35.5 -1
-0.5 t=t* 0 0.5 t [s]
1
1.5
2
-0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
Figure 10. Typical cooling gradients at the notch tip measured during the fatigue tests.
1
32.5 32 T [ C]
70.0
an = 170 MPa Nf = 1.49·104 cycles = -2.93 °C/sfL = 10 Hz rn = 0.5 mm
60.0 50.0
40.0
31.5
30.0
31
20.0
30.5
10.0
F [kN]
33
0.0
30 2.7 kN
29.5 29 -0.75
temperature signal
-10.0
load cell signal
-20.0 -30.0
-0.5
-0.25
0 t=t*
0.25 0.5 t [s]
0.75
1
1.25
1.5
Figure 11. Definition of the time t* when the machine is assumed to stop cycling and the cooling gradient is evaluated.
2.00
Q [MJ/(m3 ·cycle]
1.00
mean values
rn =3 mm
rn =1 mm 0.10 0.01
san MPa an = 130 = 130
MPa san = 150 MPa an = 150 MPa san MPa MPa rn =0.5 mm an = 170 = 170 san MPa MPa an = 130 = 130 san MPa MPa an = 150 = 150
an = 150 MPa MPa σan = 150 an = 170 MPa MPa san = 170 an = 190 MPa MPa san = 190 an = 130 MPa MPa san = 130 an = 150 MPa MPa san = 100
0.1 N/Nf Figure 12. Specific heat loss measured during the fatigue tests.
1
10
Q [MJ/(m3 ·cycle)]
Data from [20] Plain material
Present work rn =3mm rn =1mm rn =0.5mm
V-notch 2=135
1 AISI 304L Scatter band: 10-90% survival probabilities, from [19] k=2.11, TQ=2.04, TN=4.50 QA,50%=0.133 MJ/(m3 cycle) (NA=2·106 cycles) R=-1 0.1 1.E+3
1.E+4 1.E+5 Nf, number of cycles to failure
1.E+6
Figure 13. Fatigue data reported in figure 6 analysed in terms of specific heat loss per cycle. Scatter band is defined for 10% and 90% survival probabilities and it is taken from [19].
0.6
b)
a) 0.4
x
0.3
Q [MJ/(m3 ·cycle)]
0.5
0.2
0.1 2.5
2
1.5
1 0.5 x [mm]
0
-0.5
Figure 14. Heat energy distribution Q(x,y) measured close to the notch tip (a) and along the notch bisector (y=0) (b) for a specimen characterized by rn=0.5 mm, an=130 MPa, N*=1.48·104 and Nf=6.76·104. Picture was taken at N=8.12·103 cycles.
0.6
b)
a)
0.4
RQ,90%
0.3
x 0.2 0.9·Q 0.8·Q0 0 0.7·Q0
Serie1 Q(x,0) Qflt(x,0) Serie2 Q0 from specimen Serie3
0.6·Q0
Q [MJ/(m3 ·cycle)]
0.5
0.1
thickness (see Figure 16)
Q0=Q(0,0)
0 2.5
2
1.5
1 x [mm]
0.5
0
Figure 15. Heat energy distribution Qflt(x,y) from Figure 14a after data filtering (a) and the relevant distribution evaluated along the notch bisector (y=0) (b). b)
a)
s
1 mm
Figure 16. Temperature distribution measured along the notch tip from the lateral view (see Figure 1) (a) and the corresponding energy distribution (b).
a)
b)
1.5
1.3
RQ,90%
1.2 1.1
x
1 0.7·Q0
Serie1 Q(x,0) Qflt(x,0) Serie2
0.8·Q0 0.9·Q 0
Q [MJ/(m3 ·cycle)]
1.4
0.9
0.8 2.5
c)
2
1.5
1 x [mm]
0.5
0
d)
1.4 1.3
1.1 1 RQ,90%
0.9
x
0.8 0 0.8·Q0.9·Q 0
0.7·Q0
0.7
Serie1 Q(x,0) Qflt(x,0) Serie2
0.6·Q0
Q [MJ/(m3 ·cycle)]
1.2
0.6
0.5 2.5
e)
2
1.5
1 x [mm]
0.5
0
f)
0.6
RQ,90%
0.4
x
0.3 0.9·Q0 0.8·Q 0 0.7·Q0
0.2
Serie1 Q(x,0) Qflt(x,0) Serie2
0.6·Q0
Q [MJ/(m3 ·cycle)]
0.5
0.1 2.5
2
1.5
1 x [mm]
0.5
0
Figure 17. Heat energy distributions at the notch tip: (a,b,) rn=3 mm, an=170 MPa, Nf=1.85·104; (c,d) rn=1 mm, an=150 MPa, Nf=1.67·104; (e,f) rn=0.5 mm, an=100 MPa, Nf=1.35·105.
AN ANALYSIS OF THE SPECIFIC HEAT LOSS AT THE TIP OF SEVERELY NOTCHED STAINLESS STEEL SPECIMENS TO CORRELATE THE FATIGUE STRENGTH D. Rigon, M. Ricotta, G. Meneghetti* University of Padova, Department of Industrial Engineering, via Venezia, 1, 35131 Padova (Italy)
*Corresponding author: [email protected]
HIGHLIGHTS
Specific heat energy is measured at notches with tip radii from 0.5 mm to 3 mm Heat energy is measured by means of an infrared camera Heat energy correlates fatigue lives of all specimens, including plain specimens Heat energy distributions close to the notch tips are also determined.
S0167-8442(17)30294-X http://dx.doi.org/10.1016/j.tafmec.2017.09.003 TAFMEC 1946
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
4 June 2017 21 August 2017 1 September 2017
Please cite this article as: D. Rigon, M. Ricotta, G. Meneghetti, An analysis of the specific heat loss at the tip of severely notched stainless steel specimens to correlate the fatigue strength, Theoretical and Applied Fracture Mechanics (2017), doi: http://dx.doi.org/10.1016/j.tafmec.2017.09.003
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AN ANALYSIS OF THE SPECIFIC HEAT LOSS AT THE TIP OF SEVERELY NOTCHED STAINLESS STEEL SPECIMENS TO CORRELATE THE FATIGUE STRENGTH D. Rigon, M. Ricotta, G. Meneghetti* University of Padova, Department of Industrial Engineering, via Venezia, 1, 35131 Padova (Italy)
*Corresponding author: [email protected]
ABSTRACT The specific heat loss per cycle (Q parameter) was used in previous works to synthesize more than one hundred experimental fatigue test results generated from plain and bluntly notched specimens made of AISI 304L stainless steel. It was shown that Q can be estimated at a point of a specimen or a component starting from the cooling gradient measured immediately after the fatigue test has been stopped. Since the cooling gradient was measured by means of thermocouple wires attached to the specimen’s surface by means of a 1.5-to-2 mm glue dot diameter, notches with tip radii greater than 3 mm were tested, because the glue dot diameter would have been too large to capture the specific heat loss at the tip of sharper notches. In this paper, the cooling gradient has been measured by means of an infrared camera, equipped with proper lens and an extender ring to achieve a 20 m/pixel spatial resolution; therefore the investigation could be extended for the first time to notch tip radii lower than 3 mm. Fully reversed axial fatigue tests have been carried out on 4-mm-thick, hot-rolled AISI 304L stainless steel specimens. As a result, the new fatigue data have been found to collapse inside the existing heat energy -based scatter band previously calibrated on blunter notches. The heat energy distribution close to the notch tip has also been investigated.
Keywords: energy dissipation, energy methods, AISI 304L, fatigue, notch effect, energy distribution
INTRODUCTION
A material subjected to cyclic loads dissipates energy, which causes an increase of the temperature. In constant amplitude fatigue tests characterized by a given stress amplitude, mean stress and stress state, the temperature of the specimen’s surface reaches a stable value that depends on the load test frequency, the specimen’s geometry and the temperature of the surroundings. Starting from this experimental evidence, some methods were developed to estimate rapidly the fatigue limit in metallic materials and components [1-5], to detect the initiation and propagation of damage in metal materials as well as in composites [6-9] and to analyse the fatigue behaviour under constant amplitude [10-12] as well as block loading [13-15]. Since the equilibrium temperature achieved during a fatigue test depends on the thermal and mechanical boundary conditions, the specific heat energy per cycle, Q, was assumed as a fatigue damage indicator [16], because it is expected to be a material property, similarly to the plastic strain hysteresis energy [17]. In [16] a theoretical model and an experimental procedure were proposed to evaluate the Q parameter, taking advantage of temperature measurements, which can be performed by using an infrared camera. In the present paper, the temperature field was measured both on the specimen’s surface (frontal view) and in the thickness (lateral view), as illustrated in Figure 1a. The reason for that will be explained later on. At the beginning of a fatigue test, the material temperature T(t) increases and then stabilises at a value,
Tst , when the thermal equilibrium is achieved between the thermal power “generated” by the material and that dissipated to the surroundings, as shown in Figure 1b. The alternating component superimposed to Tm ( t ) is due to the thermoelastic effect. By applying the energy balance equation to a control volume V of a material undergoing a fatigue test (see Figure 2), the first law of thermodynamics applied over one loading cycle can be written as [16]:
W dV Q U dV V
(1)
V
W being the input mechanical energy per cycle (the area within the hysteresis loop), Q the dissipated thermal energy and U the variation of internal energy. Eq 1 can be written by considering the mean power exchanged over one loading cycle:
ij dij f L dV H dV c
V
V
V
Tm t E p dV t
(2)
where fL is load test frequency, H=QfL is the thermal power dissipated by conduction, convection and radiation, the material density, c the specific heat and E p the rate of accumulation of damaging energy in a unit volume of material. Since Eq. (2) considers the rate of energy contributions averaged over one cycle, thermoelasticity does not produce a net energy dissipation or absorption, because it consists of a reversible exchange between mechanical and thermal energy over one loading cycle. Therefore, the mean temperature evolution Tm ( t ) appears on the right side of Eq. 2. When temperature stabilises (t > ts in Figure 1b), the first derivative of Tm ( t ) becomes null, therefore Eq.2 simplifies to:
ij dij f L dV H dV E p dV V
V
(3)
V
If referred to a point on the specimen’s surface, Eq. 3 becomes
W fL H E p
(4)
Suppose now to stop suddenly the fatigue test at t=t* (see Figure 1b): then just after t* (i.e. at t=t*+)
the mechanical input power W f L and the rate of accumulation of fatigue damage E p will vanish. By writing the energy balance equation (2) again, we obtain:
c
T( t ) H t t ( t*)
(5)
It is worth noting that the thermal power H dissipated to the surroundings just before and just after t* is the same in Eq. (4) and in Eq. (5), respectively, because the temperature field is continuous through t*. Finally, the thermal energy released in a unit volume of material per cycle can be calculated by simply accounting for the load test frequency, fL:
c Q
H fL
T( t ) t t ( t*)
(6)
fL
Equation (6) enables one to measure readily and in-situ the specific heat loss Q at any point of a specimen or a component undergoing fatigue loadings. The Q parameter was adopted to synthesise 140 experimental results obtained from constant amplitude, push-pull, stress- or strain-controlled fatigue tests carried out on plain and notched hot rolled AISI 304L stainless steel specimens [18-20] as well as from cold drawn un-notched bars of the same steel, under fully-reversed axial or torsional fatigue loadings [21]. Later on, the mean stress influence in fatigue has also been taken into account [22]. The fatigue test results synthesised in term of Q are reported in Figure 3: all of them fall in a single energy-based scatter band, which was originally fitted only on the fatigue test results relevant to plain material, hole specimens, U and bluntly V-notched specimens [19]. Since in refs [18-20] the cooling gradients were measured by
means of thermocouple wires attached to the specimen’s surface by means of a 1.5-to-2 mm glue dot diameter, notches with tip radii greater than 3 mm were tested ,because the glue dot diameter would have been too large to capture the specific heat loss at the tip of sharper notches. In this paper, the use of the specific energy Q has been extended to more severe notches, taking advantage of the much improved spatial resolution provided by the adopted infrared camera. Therefore, specimens characterized by 3, 1 and 0.5 mm notch tip radii have been tested. As a result, the new fatigue data were seen to collapse inside the existing heat energy-based scatter band previously calibrated. Finally, the energy distribution around the notch tip Q(x,y) was investigated and it was found that the gradient of Q(x,y) tends to level off while approaching the notch tip.
MATERIAL AND TEST METHOD
Constant amplitude, completely reversed, stress-controlled fatigue tests were carried out on 4-mm thick, hot rolled AISI 304L stainless steel specimens, having notch tip radii r n equal to 3, 1, and 0.5 mm, as reported in Figure 4a. The mechanical properties and the chemical composition are reported in Table 1 [20], while Figure 4b shows the austenitic microstructure of the material. The analysed stainless steel had a material density and the specific heat c equal to 7940 kg/m3 and 507 J/(kg K), respectively [15,23]. Starting from 46 x 150 mm rectangular plates, notches were obtained by wire electro discharge machining, followed by electrochemical polishing. After that, the specimen surfaces were polished using progressively finer emery papers (until the maximum paper grade of 4000 was reached), in order to prepare the surface for fatigue crack monitoring. One surface of the specimen as well as the notch root in the thickness direction were black painted to increase the material emissivity in view of the infrared thermal acquisitions, as will be discussed in the next sections.
The net-section stress concentration factors, Ktn, were evaluated by carrying out 3D linear elastic finite element analyses and resulted 3.41, 4.85 and 6.10, for r n equal to 3, 1 and 0.5 mm, respectively. To take into account the machine grip effect, displacements were applied to the relevant lines shown in Figure 4a. The fatigue tests were carried out by using a servo-hydraulic Schenck Hydropuls PSA 100 machine having a 100 kN load cell and equipped with a TRIO Sistemi RT3 digital controller. Load test frequencies were set in the range between 3 and 40 Hz, depending on the applied stress level, in order to keep the material temperature below 60 °C. A total number of 25 specimens was fatigue tested,and the number of cycles to failure, Nf, was equal to that for complete separation. The temperature field T(x,y) close to the notch apex (see the “frontal view in Figure 1a) was measured by using a FLIR SC7600 infrared camera, operating at a frame rate, facq, equal to 200 Hz, having a 1.5-5.1 m spectral response range, 50 mm focal lens, a noise equivalent temperature difference (NETD) < 25 mK and an overall accuracy of 0.05°C. It was equipped with an analog input interface, which was used to synchronize the force signal coming from the load cell with the temperature signal. Furthermore, a 30-mm-long extender ring was adopted to achieve a spatial resolution of approximately 20 m/pixel. Due to the presence of the extender ring, the Field of View (FoV) was reduced to 320x256 pixels. To avoid vignetting, the temperature field around the notch tip was acquired by positioning the notch tip itself in the centre of the Field of View (FOV). Infrared images were analyzed by means of the ALTAIR 5.90.002 commercial software. To monitor the evolution of Q during each test, 1 to 10 cooling gradients (depending on the applied stress levels) were performed using a 10-second-long sampling window, translating into 2000 acquired frames, the frame rate being facq=200 Hz. More precisely, acquisitions consisted of approximately 5 seconds of running test (1000 frames between t s and t* in Figure 1b) followed by the machine stop at the time t*, and the remaining 5 seconds, during which the cooling gradient was captured and additional 1000 frames were acquired . The machine test was stopped by using a manual trigger signal. The span rate of the test machine was set to 100% to induce a test stop as
abrupt as possible. Qualitatively, it took approximately two tapered force cycles to reach a complete stop as depicted in Figure 11, which will be commented in the next paragraph. After the test stop, the set point of the machine was kept to the zero load level during the cooling phase. The crack length was measured by means of a AM4115ZT Dino-lite digital microscope operating with a magnification ranging from 20x to 220x. The microscope and the infrared camera monitored the opposite surfaces of the specimens, as shown in Figure 5.
FATIGUE TEST RESULTS AND ENERGY-BASED ANALYSIS
All fatigue test results, presented elsewhere by the authors [24], are summarised in Figure 6 in terms of net-section stress amplitude, an. The 10%-90% Survival Probability (PS) scatter band reported in the figure was originally calibrated in [19], by considering fatigue test results carried out on Uand V-notched (2 = 90°, see Figure 1a) specimens with tip radii equal to 5 mm and 3 mm, respectively, and assuming a log-normal distribution of the number of cycles to failure with a 95% confidence level. The mean curve, the inverse slope k, the stress-based scatter index T (an10%/an90%) and the life-based index TN, (TN,Tk) are also reported. It can be seen that the new experimental results fall inside the previously defined scatter band. However, plain specimens exhibit higher fatigue strength, as reported in Figure 6. To illustrate the evolution of the surface temperature, long-term acquisitions were performed for three specimens, equipped with copper-constantan thermocouple wires having diameter 0.127 mm, which were fixed at a distance of 5 mm above the notch tip (see Figure 7), by means of a silver loaded conductive epoxy glue. A low sample rate of 2 Hz was adopted by using a Agilent HP 34970A data logger. Results reported in Figure 7 are just exemplary data, which were not processed further. It is worth noting that in this figure the thermoelastic effect could not be measured, because
the sample rate adopted to acquire the temperature signal was too low as compared to the frequency of the thermoelastic temperature, which obviously coincided with the load test frequency fL. Figure 7 shows that several stops were done during a single fatigue test, until a fatigue crack emanating from the notch tip was detected by the digital microscope. The first crack detected in the case of specimens V_135_R3_07 and V_135_R3_08 are shown in Figure 8. After detecting a crack for the first time, having length “a“ at a number of cycles N* reported in Figure 7, the fatigue test was run to final failure without further stops and cooling gradient measurements. Figure 7 shows that temperature was not stabilised before the test stop, as opposed to the situation illustrated in previous Figure 1b. Therefore, the internal energy term associated to the time derivative of Tm(t) on the right hand side of Eq. (2) is different from zero. As a conclusion, Equations from 3 to 6 should not be applied, strictly speaking, because they assume that the time derivative of T m(t) is zero. However, by considering as an example the test stop highlighted in Figure 7 and the relevant temperature acquisitions reported in the next Figure 10a, it could be verified that the cooling gradient just after t* is 24 times higher than the heating gradient (i.e. dTm/dt) just before t*. Therefore, of the total heat production, the dissipated fraction is by far greater than the self-heating fraction. Given that, Equations 3 to 6 were considered to be applicable in an engineering sense. During each fatigue test several test stops were performed before N* to monitor the evolution of the energy parameter Q, according to Eq (6). Typical examples of temperature maps captured at the notch tips at time t=t* (see Figure 1b) are shown in Figure 9, for different notch radii and applied nominal stress amplitude, an. Figure 9 highlights that the maximum temperature was achieved in the case of the highest stress amplitude and the greatest notch radius (Figure 9a), where heat generation involves a certain volume of material embracing the notch tip. In this case, the load test frequency was set sufficiently low to limit the maximum material temperature below 60 °C, as mentioned above. Figure 10a-f shows the temperature versus time acquisitions relevant to Figure 9a-f, respectively. In particular, Figure 10 reports the maximum temperature Tmax extracted frame-
by-frame from a circular area embracing the notch, as shown in the detail of Figure 4a: essentially Tmax is the temperature at the notch tip. It can be seen that for the notch tip radii analysed, the time window considered to calculate the cooling gradient is of the order of one tenth of a second and the corresponding temperature decrease is of the order of some tenths of a degree. In Figure 10a-f it can be observed that the test machine takes some tenths of a second to completely stop cycling. As a consequence, the force as well as the associated thermoelastic signals reduce in a tapered way, as illustrated in Figure 11. Therefore an operational definition of the time t* was adopted, when the test machine was assumed to stop cycling and the cooling gradient was measured. Such a definition was as follows: t* is the time (after triggering the machine stop) when the first force peak is within a range of ±2.7 kN. In all experimental situations analysed in the present work, it was verified that the first peak within the range ±2.7 kN was below 5% of the force amplitude applied during the relevant fatigue test. The evolution of heat energy Q versus the fatigue life normalised with respect to Nf is reported in Figure 12, which highlights a range of values from 0.28 to 1.73 MJ/(m3cycle), that means a factor of 6.18. In view of this body of evidence, the Q parameter can be assumed reasonable constant during a single fatigue test, as compared to the wide range of energy levels measured for the different applied net-stress amplitudes. Therefore, the fatigue tests results were reanalysed in terms of average Q, taken from Figure 12. Figure 13 shows that the new fatigue data fall inside the existing heat energy -based scatter band previously calibrated on blunter notches [19]. Plain material data fall in the same scatter band, as opposed to previous Figure 6.
HEAT ENERGY DISTRIBUTION CLOSE TO THE NOTCH TIP
Additional analyses were performed to investigate the energy distribution close to the notch tip, because this topic might be of interest in view of applying the proposed approach to pointed V-
notches, including crack propagation analyses. Investigations in this direction have been performed recently [20,24,25], because it is well known that stress-/strain- or strain energy density-based approaches take into account the distributions (and not just peak values) of the adopted fatiguerelevant parameter. Having measured the temperature maps close to the notch tip, as reported in previous Figure 9, the distribution of the energy parameter Q(x,y) could be calculated taking advantage of a numerical procedure developed in Matlab® environment, which calculated pixel-by-pixel the cooling gradient according to Eq. 6. After some preliminary analyses, for the sake of simplicity the time-window adopted to evaluate the cooling gradient was chosen equal to 0.1s and it was kept constant for all pixels processed. Figure 14a shows as an example the energy distribution Q(x,y) measured at N=8.12·103 cycles in the case of a specimen having r n=0.5 mm, a=130 MPa and Nf =6.76·104 cycles, while Figure 14b shows the distribution Q(x,0) along the notch bisector, starting from the notch tip (x=0). Figure 14a shows that the specimen edge is not well defined due to the well-known edge effect characteristic in thermography (see [26] as an example). Therefore, the picture taken with the digital microscope on the opposite side of the specimen was used to single-out the notch tip location and to transfer it at the co-ordinates (x=0, y=0) reported in Figure 14a. A gentle scratch made on both surfaces of the specimens at the same distance from the free edge made transferability possible. After positioning the notch tip at (x=0, y=0), the negative portion of the picture (x<0) was removed, as it will be seen in the next Figures 15 and 17. Figures 14a and 14b show that a certain level of noise exists; therefore, in order to smooth the energy fields, raw data shown in Figure 14 were filtered by applying the “imgaussfilt” function available in Matlab® code, so that a much smoother heat distribution Q flt(x,y) was obtained. Figure 15 reports the result obtained after processing the data reported in Figure 14 and shows that the gradient of the thermal energy tends to decrease while approaching the notch tip, where the maximum energy dissipation Q0=Q(0,0) exists.
To support the peak thermal energy just evaluated at the notch tip, during the fatigue test carried out on the specimen to which Figure 14 is referred to, thermal maps were taken both from the frontal and from the lateral views (see Figure 1a). More precisely, after a given test stop to acquire the cooling phase from the frontal view, the specimen was turned 90° and the test was restarted, followed shortly after by a new stop to acquire the cooling gradient from the lateral view. Figure 16a shows the temperature distribution at the notch tip taken from the lateral view and Figure 16b shows the Q values measured at different locations along the specimen thickness, resulting in a mean value Q=0.55 MJ/(m3cycle). Such a value has been reported at x=0 in Figure 15b and it is seen in excellent agreement with the value calculated at the notch tip from the energy distribution measured at the specimen surface. Figure 15a reports also the constant-Q contours; in particular, a circular contour is plotted, which identifies the biggest region where the dissipated energy is equal to or higher than 90% the maximum energy calculated at the notch tip, Q0. In figure 15a the size of such circular region is RQ,90%=0.54 mm. Figure 17 reports the energy distributions Q(x,y) as well as the distributions along the notch bisector Q(x,0) for other specimens characterised by different notch radii and applied stress amplitudes. A selection of results is also summarised in Table 2 and it is seen that RQ,90% ranges from 0.53 to 0.87 mm. In a previous work, the structural volume size for fatigue strength estimations was evaluated for the same material and test conditions and it resulted equal to 0.52 mm [25]. Living aside the definition of the structural volume and the description of the fatigue strength criterion, which are out of the scope of the present paper, the results found here support the conclusion that the energy dissipation for the present material, notch geometries and testing conditions is reasonably constant inside the structural volume.
CONCLUSIONS
In order to extend the heat energy-based approach to more severely notched specimens as compared to those tested previously, constant amplitude, completely reversed, stress-controlled fatigue tests have been carried out on hot rolled, 4-mm-thick notched specimens made of AISI 304L stainless steel specimens having notch tip radii equal to 3, 1, and 0.5 mm. The specific heat energy Q was evaluated at the notch tip by means of an infrared camera with a spatial resolution equal to 20 m/pixel. Several evaluations were performed during a fatigue test, until the initiation of a crack was detected by means of a digital microscope. As a result, the specific heat loss Q was seen to be approximately constant during individual fatigue tests. This outcome has an important practical consequence, in that fatigue life can be anticipated starting from measurement performed at the beginning of the fatigue test. If presented in terms of specific heat energy at the notch tip versus the number of fatigue cycles to failure, the new experimental data were seen to fall inside the energy-based scatter band calibrated previously by the authors on fatigue data obtained on plain as well as notched specimens, characterised by larger notch tip radii than those tested in the present contribution. Finally, the heat energy distribution close to the notch tip was also investigated by estimating the size of the region near the notch tip where energy dissipation is equal to or greater than 90% the maximum value existing at the notch apex. Such region was assumed to be circular and centered at the notch tip. It was found that for the analysed material, notch geometries and testing conditions, its radius is equal to some tenths of a millimetre.
ACKNOWLEDGEMENTS This work was carried out as a part of the project CODE CPDA145872 of the University of Padova. The Authors would like to express their gratitude for financial support.
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AN ANALYSIS OF THE SPECIFIC HEAT LOSS AT THE TIP OF SEVERELY NOTCHED STAINLESS STEEL SPECIMENS TO CORRELATE THE FATIGUE STRENGTH D. Rigon, M. Ricotta, G. Meneghetti* University of Padova, Department of Industrial Engineering, via Venezia, 1, 35131 Padova (Italy)
*Corresponding author: [email protected]
CAPTIONS TO TABLES AND FIGURES Table 1: Mechanical properties and chemical composition of the hot-rolled AISI 304L stainless steel. Table 2: Value of radius RQ,90% measured during the fatigue test.
Figure 1. Experimental set-up adopted (a) and evaluation of the cooling gradient (from Eq. (1)) during a fatigue test (b) Figure 2. Energy balance of a material subjected to cyclic loading. Figure 3. Fatigue tests results in terms of specific heat energy. The scatter band was calibrated only on data published in [19]. Figure 4. Specimen geometry (thickness is 4mm, 2=135°) (a) and AISI 304L austenitic microstructure (b). Figure 5. Test setup consisting of a FLIR SC7600 infrared camera, a AM4115ZT Dino-lite digital microscope and the specimen clamped in the test machine. Figure 6. Fatigue data analysed in terms of net-section stress amplitude. Scatter band was calibrated in [19]. Figure 7. Typical temperature evolution measured at a distance of 5 mm from the notch apex by using thermocouples. Figure 8. Crack inspection by using the digital microscope for two of the fatigue tests reported in Figure 7 characterised by an = 190 MPa, N* = 3.20·103 cycles (a) and an = 180 MPa, N* = 7.86•103 cycles (b). Figure 9. Temperature maps observed during the fatigue tests. Figure 10. Typical cooling gradients at the notch tip measured during the fatigue tests. Figure 11. Definition of the time t* when the machine is assumed to stop cycling and the cooling gradient is evaluated. Figure 12. Specific heat loss measured during the fatigue tests. Figure 13. Fatigue data reported in figure 6 analysed in terms of specific heat loss per cycle. Scatter band is defined for 10% and 90% survival probabilities and it is taken from [19].
Figure 14. Heat energy distribution Q(x,y) measured close to the notch tip (a) and along the notch bisector (y=0) (b) for a specimen characterized by rn=0.5 mm, an=130 MPa, N*=1.48·104 and Nf=6.76·104. Picture was taken at N=8.12·103 cycles. Figure 15. Heat energy distribution Qflt(x,y) from Figure 14a after data filtering (a) and the relevant distribution evaluated along the notch bisector (y=0) (b). Figure 16. Temperature distribution measured along the notch tip from the lateral view (see Figure 1) (a) and the corresponding energy distribution (b). Figure 17. Heat energy distributions at the notch tip: (a,b,) rn=3 mm, an=170 MPa, Nf=1.85·104; (c,d) rn=1 mm, an=150 MPa, Nf=1.67·104, (e,f) rn=0.5 mm, an=100 MPa, Nf=1.35·105.
Table 1: Mechanical properties and chemical composition of the hot-rolled AISI 304L stainless steel. Rp0.2%
Rm
A
A,-1,50%
(MPa)
(MPa)
(%)
(MPa)
279
620
57
202
HB
170
C
Mn
Si
Cr
Ni
P
S
N
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
0.026
1.470
0.370
18.1
8.2
0.034
0.001
0.058
Table 2: Value of radius RQ,90% measured during the fatigue test. rn
an
fL
Nf
N*/Nf
Q0
RQ,90% 3
[mm]
[MPa]
[Hz]
3
190
10
7.82·103
3
170
10
3
110
1
N/Nf
[MJ/(m cycle)]
[mm]
0.41
1.98
0.85
0.24
1.85·104
0.61
1.45
0.87
0.42
25
2.71·105
0.67
0.38
0.55
0.17
150
10
1.67·104
0.33
1.17
0.64
0.28
1
120
15
7.68·104
0.40
0.42
0.55
0.13
0.5
190
5
8.17·103
0.40
1.77
0.83
0.21
0.5
100
35
1.35·105
0.13
0.51
0.53
0.08
0.5
130
25
6.76·104
0.22
0.55
0.54
0.12
a)
b)
F(t) T(x,y;t)
T(t) Tmax infrared camera (frontal view)
y 2 Tst
x
t
Tm(t)
infrared camera (lateral view)
ts
t*
t t
t
Figure 1. Experimental set-up adopted (a) and evaluation of the cooling gradient (from Eq. (1)) during a fatigue test (b)
F(t) W
V
n
U
Q
Figure 2. Energy balance of a material subjected to cyclic loading.
100 Scatter band: 10-90% survival probabilities, from [19] k=2.11, TQ=2.04, TN=4.50 QA,50%=0.133 MJ/(m3 cycle) R=-1
Q [MJ/(m3 cycle)]
10
Data from [21] Axial load Torsional load Data from [20] Plain material rn =3mm V-notch rn =1mm 2=90 rn =0.5mm
k 1
AISI 304L 1
0.1
Data from [19] Plain specimens Stair-case: broken, unbroken Hole, rn =8mm U-notch, rn =5mm Blunt V-notch, 2=90 , rn =3mm + Strain controlled
0.01 1.E+2
1.E+3
≈ 140 test results
1.E+4 1.E+5 1.E+6 Nf, number of cycles to failure
1.E+7
1.E+8
Figure 3. Fatigue tests results in terms of specific heat energy. The scatter band was calibrated only on data published in [19]. a)
b) Machine grip
Area from which Tmax was extracted
rn rn 2
150 90
8 50 m
46
Machine grip
Figure 4. Specimen geometry (thickness is 4mm, 2=135°) (a) and AISI 304L austenitic microstructure (b).
Digital microscope
Infrared camera
Figure 5. Test setup consisting of a FLIR SC7600 infrared camera, a AM4115ZT Dino-lite digital microscope and the specimen clamped in the test machine.
500 plain material from [20], k=17.2 A, 1,50%= 202 MPa
an [MPa]
1 100
k
AISI 304L R=-1 Scatter band: 10-90% survival probabilities, from [19] k=5.8, T=1.30, TN=4.60 Present work rn =3 mm, Ktn = 3.41 rn =1 mm, Ktn = 4.85 rn =0.5 mm, Ktn = 6.10 10 1.E+3
1.E+4
Short stair-case unbroken, broken
V-notch 2=135
1.E+5 1.E+6 Nf, number of cycles to failure
1.E+7
1.E+8
Figure 6. Fatigue data analysed in terms of net-section stress amplitude. Scatter band was calibrated in [19].
100 90
N* (a = 0.17 mm)
80
N* (a = 0.25 mm)
70
a
Test stop (see Figure 10a)
60 T [ C]
thermocouple
N* (a = 0.13 mm)
5 m m
50 40
30 V_135_R3_07 an = 190 MPa, fL= 5 10 Hz V_135_R3_08 an = 180 MPa, fL= 10 Hz V_135_R3_06 an = 170 MPa, fL= 10 Hz
20 10 0 0
5000
10000 N, number of cycles
15000
20000
Figure 7. Typical temperature evolution measured at a distance of 5 mm from the notch apex by using thermocouples.
a)
b)
Crack tip
Crack tip 200 m
200 m
Figure 8. Crack inspection by using the digital microscope for two of the fatigue tests reported in Figure 7 characterised by an = 190 MPa, N* = 3.20·103 cycles (a) and an = 180 MPa, N* = 7.86·103 cycles (b).
rna)= 3 mm, an = 190 MPa, fL = 10 Hz
b) rn = 3 mm, an = 110 MPa, fL = 25 Hz
500 m
c) rn = 1 mm, an = 150 MPa, fL = 10 Hz
500 m
d) rn = 1 mm, an = 120 MPa, fL = 15 Hz
500 m
500 m
rn = 0.5 mm, an = 190 MPa, fL = 5 Hz e)
f) rn = 0.5 mm, an = 100 MPa, fL = 35 Hz
500 m
Figure 9. Temperature maps observed during the fatigue tests.
500 m
53 52.5 52
Tmax [ C]
b) 42
an = 190 MPa Nf = 7.82·103 cycles fL = 10 Hz t t t
51.5
= 0.20 °C/s
51 50.5
t t t
= -4.81 °C/s
50
41
t t t
= -2.02 °C/s
40.5 rn = 3 mm
49.5
rn = 3 mm
49
40 -0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
c) 40.5
1
t t t
33.8
39
38.5 38
= -1.67 °C/s
t t t
33.4
33.2 33
rn = 1 mm
1
an = 120 MPa Nf = 7.68 ·104 cycles fL = 15 Hz
33.6
= -2.80 °C/s
Tmax [ C]
39.5
-0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s] d) 34
an = 150 MPa Nf = 1.67·104 cycles fL = 10 Hz
40 Tmax [ C]
an = 110 MPa Nf = 2.71·105 cycles fL = 25 Hz
41.5 Tmax [ C]
a)
rn = 1 mm
32.8 -0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
e) 39.5
1 f) 38.5
an = 190 MPa Nf = 8.17·103 cycles fL = 5 Hz
39
-0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
38
1
an = 100 MPa Nf = 1.35·105 cycles fL = 35 Hz
t t t
= -1.75 °C/s
Tmax [ C]
Tmax [ C]
37.5 38.5 38
37.5
37
37
= -4.11 °C/s
36.5 36
rn = 0.5 mm
t t t
rn = 0.5 mm
35.5 -1
-0.5 t=t* 0 0.5 t [s]
1
1.5
2
-0.5 -0.25 t=t* 0 0.25 0.5 0.75 t [s]
Figure 10. Typical cooling gradients at the notch tip measured during the fatigue tests.
1
32.5 32 T [ C]
70.0
an = 170 MPa Nf = 1.49·104 cycles = -2.93 °C/sfL = 10 Hz rn = 0.5 mm
60.0 50.0
40.0
31.5
30.0
31
20.0
30.5
10.0
F [kN]
33
0.0
30 2.7 kN
29.5 29 -0.75
temperature signal
-10.0
load cell signal
-20.0 -30.0
-0.5
-0.25
0 t=t*
0.25 0.5 t [s]
0.75
1
1.25
1.5
Figure 11. Definition of the time t* when the machine is assumed to stop cycling and the cooling gradient is evaluated.
2.00
Q [MJ/(m3 ·cycle]
1.00
mean values
rn =3 mm
rn =1 mm 0.10 0.01
san MPa an = 130 = 130
MPa san = 150 MPa an = 150 MPa san MPa MPa rn =0.5 mm an = 170 = 170 san MPa MPa an = 130 = 130 san MPa MPa an = 150 = 150
an = 150 MPa MPa σan = 150 an = 170 MPa MPa san = 170 an = 190 MPa MPa san = 190 an = 130 MPa MPa san = 130 an = 150 MPa MPa san = 100
0.1 N/Nf Figure 12. Specific heat loss measured during the fatigue tests.
1
10
Q [MJ/(m3 ·cycle)]
Data from [20] Plain material
Present work rn =3mm rn =1mm rn =0.5mm
V-notch 2=135
1 AISI 304L Scatter band: 10-90% survival probabilities, from [19] k=2.11, TQ=2.04, TN=4.50 QA,50%=0.133 MJ/(m3 cycle) (NA=2·106 cycles) R=-1 0.1 1.E+3
1.E+4 1.E+5 Nf, number of cycles to failure
1.E+6
Figure 13. Fatigue data reported in figure 6 analysed in terms of specific heat loss per cycle. Scatter band is defined for 10% and 90% survival probabilities and it is taken from [19].
0.6
b)
a) 0.4
x
0.3
Q [MJ/(m3 ·cycle)]
0.5
0.2
0.1 2.5
2
1.5
1 0.5 x [mm]
0
-0.5
Figure 14. Heat energy distribution Q(x,y) measured close to the notch tip (a) and along the notch bisector (y=0) (b) for a specimen characterized by rn=0.5 mm, an=130 MPa, N*=1.48·104 and Nf=6.76·104. Picture was taken at N=8.12·103 cycles.
0.6
b)
a)
0.4
RQ,90%
0.3
x 0.2 0.9·Q 0.8·Q0 0 0.7·Q0
Serie1 Q(x,0) Qflt(x,0) Serie2 Q0 from specimen Serie3
0.6·Q0
Q [MJ/(m3 ·cycle)]
0.5
0.1
thickness (see Figure 16)
Q0=Q(0,0)
0 2.5
2
1.5
1 x [mm]
0.5
0
Figure 15. Heat energy distribution Qflt(x,y) from Figure 14a after data filtering (a) and the relevant distribution evaluated along the notch bisector (y=0) (b). b)
a)
s
1 mm
Figure 16. Temperature distribution measured along the notch tip from the lateral view (see Figure 1) (a) and the corresponding energy distribution (b).
a)
b)
1.5
1.3
RQ,90%
1.2 1.1
x
1 0.7·Q0
Serie1 Q(x,0) Qflt(x,0) Serie2
0.8·Q0 0.9·Q 0
Q [MJ/(m3 ·cycle)]
1.4
0.9
0.8 2.5
c)
2
1.5
1 x [mm]
0.5
0
d)
1.4 1.3
1.1 1 RQ,90%
0.9
x
0.8 0 0.8·Q0.9·Q 0
0.7·Q0
0.7
Serie1 Q(x,0) Qflt(x,0) Serie2
0.6·Q0
Q [MJ/(m3 ·cycle)]
1.2
0.6
0.5 2.5
e)
2
1.5
1 x [mm]
0.5
0
f)
0.6
RQ,90%
0.4
x
0.3 0.9·Q0 0.8·Q 0 0.7·Q0
0.2
Serie1 Q(x,0) Qflt(x,0) Serie2
0.6·Q0
Q [MJ/(m3 ·cycle)]
0.5
0.1 2.5
2
1.5
1 x [mm]
0.5
0
Figure 17. Heat energy distributions at the notch tip: (a,b,) rn=3 mm, an=170 MPa, Nf=1.85·104; (c,d) rn=1 mm, an=150 MPa, Nf=1.67·104; (e,f) rn=0.5 mm, an=100 MPa, Nf=1.35·105.
AN ANALYSIS OF THE SPECIFIC HEAT LOSS AT THE TIP OF SEVERELY NOTCHED STAINLESS STEEL SPECIMENS TO CORRELATE THE FATIGUE STRENGTH D. Rigon, M. Ricotta, G. Meneghetti* University of Padova, Department of Industrial Engineering, via Venezia, 1, 35131 Padova (Italy)
*Corresponding author: [email protected]
HIGHLIGHTS
Specific heat energy is measured at notches with tip radii from 0.5 mm to 3 mm Heat energy is measured by means of an infrared camera Heat energy correlates fatigue lives of all specimens, including plain specimens Heat energy distributions close to the notch tips are also determined.