Fatigue strength of autofrettaged Diesel injection system components under elevated temperature

Accepted Manuscript Fatigue Strength of Autofrettaged Diesel Injection System Components Under Elevated Temperature Michael Vormwald, Teresa Schlitzer, Darko Panic, Heinz Thomas Beier PII: DOI: Reference:

S0142-1123(18)30038-0 https://doi.org/10.1016/j.ijfatigue.2018.01.031 JIJF 4560

To appear in:

International Journal of Fatigue

Received Date: Revised Date: Accepted Date:

15 December 2017 24 January 2018 28 January 2018

Please cite this article as: Vormwald, M., Schlitzer, T., Panic, D., Thomas Beier, H., Fatigue Strength of Autofrettaged Diesel Injection System Components Under Elevated Temperature, International Journal of Fatigue (2018), doi: https://doi.org/10.1016/j.ijfatigue.2018.01.031

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Fatigue Strength of Autofrettaged Diesel Injection System Components Under Elevated Temperature Michael Vormwald, Teresa Schlitzer, Darko Panic, Heinz Thomas Beier Materials Mechanics Group, Technische Universität Darmstadt, Franziska-Braun-Str. 3, D-64287 Darmstadt, Germany

Abstract: The influence of elevated temperature, typical for operating fuel injection systems of Diesel engines, on the fatigue strength of such systems is the subject of the current paper. The investigation covered components, whose original durability had been increased by the mechanical procedure of autofrettage (unique mechanical overload). The method introduces favorable, fatigue strength increasing compressive residual stresses. No validated information was available concerning the influence of temperature on the fatigue strength of such components with residual stresses for the temperature up to 180 °C. The transient cyclic material behavior of the steel 42CrMo4 (used for autofrettaged components) was investigated as a function of the test temperature. The influence of elevated operating temperature on the fatigue strength of autofrettaged and non-autofrettaged components was simulated for intersecting hole specimens applying fracture mechanics based approaches of various complexity. The results were compared with results of an experimental investigation. The accuracy of all simulation models has been very satisfying.

Keywords: Autofrettage, fatigue crack growth, crack arrest, crack closure, cyclic plasticity

1

1 Introduction Raising the efficiency of engines is a major demand stemming from economic and even more from ecologic imperatives. For Diesel engines this goal can be strived by increasing the injection pressure. Therefore, injection pumps, fuel pipes, common rails and injectors have to sustain higher and higher cyclic pressures. As soon as the loading is predefined – here the cyclic injection pressure ranges – the engineer has to elaborate an appropriate design to fulfill the requirements concerning the fatigue life of the components. The remaining options are the choices of material and geometry. Materials used in this technical field are either low alloyed steels quenched and tempered to achieve an ultimate tensile strength of approximately 1000 MPa or case-hardened steels which are applied in the high strength condition in the highly stressed notch and surface areas of the components. In the current investigation the steel 42CrMo4 was used with an ultimate tensile strength of 1264 MPa. Higher strength steels are now under examination with a crucial look on their ductility. Despite this, the current optimal balance between strength and ductility was assumed to be provided by the steel under consideration. The maximum stresses and strains in components loaded by internal pressure can only be decreased to a limited amount by increasing the wall thickness. The inner diameters are fixed by serviceability requirements. Meanwhile further increase of the outer diameter does no longer efficiently reduce the highest stresses (which are found at the inner surface) if the ratio of outer and inner diameter exceeds values of approximately two to three. The remaining tools for increasing the components’ fatigue strength are limited to methods concerning the production process. For example reducing the surface roughness is one of the methods applied. However, polishing inner wall surfaces is complicated and expensive. The method of choice is autofrettage. Autofrettage is a local surface strengthening procedure to enhance the fatigue resistance of pressurized components. It has been used since the beginning of the 20th century. The beneficial effect of the autofrettage is based on compressive residual stresses, which are induced by a single 2

pressure overload applied as a final step during production. This autofrettage pressure overload is much higher than the subsequent operating pressure. More than a decade ago the state of the art has been summarized in reference [1]. The principles have not changed since. The autofrettage pressure leads to large plastic deformations, i.e. elongations, in the highly stressed regions of the component. After unloading compressive residual stresses prevail in these regions. The cyclic operating pressure leads to tensile stresses at the critical locations, however, these stresses first have to reduce the compressive residual stresses. Therefore, they are less damaging than in a state without compressive residual stresses. Consequently, the fatigue strength expressed in terms of sustainable operating pressure ranges is increased. Incidentally, the French verb “fretter” describes heat-shrinking of rings around vessels. The circumference of the rings is shorter than the vessel’s circumference. A compressive (residual) hoop stress is introduced into the vessel increasing its resistance against internal pressure. The initial overpressure shrinks virtual rings by itself, in Greek . The noun “autofrettage” is created. In Diesel engine injection technology crucial designs are provided containing intersecting holes, e.g. in common rails and injectors. Therefore, the present investigation focused on the geometry of two holes with identical diameter intersecting at an angle of 90°, similar to the situation in common rails. Accurate methods for calculating the fatigue strength of such components have been presented previously [2][3][4]. However, the influence of an elevated temperature has been neglected. The components of interest are operated near the combustion chambers. For example for injectors the temperature has been measured to reach values of 180 °C. The current investigation was therefore focused on determining and modeling the temperature influence on the fatigue strength. The complete results of the research project are presented in a report [5] where further details concerning the major results may be found. Research related to autofrettage is mainly focused on the simulation of residual stresses. It is pointed out that Bauschinger’s effect must not be neglected [6][7][8][9][10][11][12]. Ma et al. [10][11] and

3

Maleki et al. [12] emphasize that powerful plasticity models are required. These authors [10][12] investigated the effect of the magnitude of the autofrettage pressure, too. Thermomechanical loading was considered by Abdelsalam and Sedaghati [13] as well as Zheng and Xuan [14], the latter paper dealing with the effect of a shakedown of residual stresses due to multiple application of the autofrettage pressure. Perl and Perry [15] as well as Troiano et al. [16] reported that a moderate heat treatment may have a positive effect. Bähre et al. [17][18][19][20] investigated the influence of the complete production chain on the development of residual stresses. Powerful plasticity models were used. The stability of residual stresses in T-shaped bore intersections was investigated in [21]. This geometry is similar to the geometry of the components in the present paper. There are fewer investigations of the effect of autofrettage on the fatigue strength. Abdelsalam and Sedaghati [13][22] present results of code [23] based fatigue life calculations. The influence of mean stress is taken into account in the fatigue crack growth rate equation formulated in terms of the stress intensity factor range. Also based on the linear elastic fracture mechanics, however in a simplified formulation, Chen et al. [24] performed Monte-Carlo-simulations to evaluate the influence of random input parameters on the fatigue life. Thumser et al. [25] investigated the fatigue strength of autotrettaged specimens similar to those of the present investigation. The methods described for evaluating the fatigue strength have been developed further in the present research work.

2 Mechanical material behavior Chemical composition and basic mechanical parameters of the material under consideration are shown in Tables 1 and 2. After machining, the specimens have been austenitised in vacuum, quenched in oil and annealed in inert gas. The temperature control of the process was chosen in accordance with special know-how for achieving an ultimate tensile strength of approximately 1200 MPa.

4

Table 1: Chemical composition of the material 42CrMo4 in % C

P

S

Si

Mn

Cr

Mo

Inspection certificate

0,406 0,017

0,009

0,30

0,76

1,20

0,28

Optical emission spectroscopy

0,422 0,016

0,013

0,32

0,74

1,23

0,28

Table 2: Mechanical material parameters of 42CrMo4 quenched and tempered, average of three tests 30 °C

120 °C

180 °C

200100

199300

199900

Ultimate tensile strength, Rm, in MPa

1264

1210

1202

Offset yield stress, Rp0,2, in MPa

1114

1024

992

Young’s modulus, E, in MPa

First, any reliable fatigue strength assessment requires knowledge of the residual stress field introduced by autofrettage. Large elastic-plastic deformations occur followed by deformations during the unloading of the component which are also of elastic-plastic nature. The material’s deformation behavior under a load and unload cycle was measured for various temperatures and maximum uniaxial strain values. Second, during subsequent operating of the component the material generally may show transient cyclic deformation behavior possibly approaching a cyclically stabilized state. During this period especially the material in the highly stressed (and therefore critical) regions undergoes a process of combined mean stress relaxation and ratcheting. This leads to a partial loss of initially introduced beneficial compressive residual stresses. The effect is more pronounced under elevated temperature. The material’s sensitivity to mean stress relaxation and ratcheting was also measured in the temperature range of interest.

5

The material model of Chaboche [26] as implemented in the commercial finite element software Abaqus was expected to realistically describe these effects. Its constitutive equations are listed below: Additive decomposition of strains, .

(1)

Elastic deformation, .

(2)

Yield condition,

.

(3)

Flow rule, .

(4)

Kinematic hardening rule, ,

(5) .

(6)

Isotropic hardening rule, .

(7)

Applying a sophisticated optimization strategy supplied the parameters shown in Table 3.

6

Table 3: Material parameters of 42CrMo4 as used in the Chaboche model 42CrMo4 T = 20 °C Young’s modulus, E, in MPa

T = 180 °C

200000

199000

0.3

0.3

1.2e-05

1.3e-05

σF in MPa

910

756.489

Rs in MPa

-283.173

-272.135

11.527

18.678

C1 in MPa

6.758e-06

4.055e-05

C2in MPa

9303

2.177e-06

C3in MPa

80269.9

83413.2

C4in MPa

4.589e-04

10432.4

C5in MPa

12295.6

10420.9

1

5123

5123

2

1281

1281

3

320

320

4

80

80

5

20

20

Poisson ratio in K-1

b

Figure 1 shows a comparison of measured and simulated stress-strain-curves for the first loading and unloading cycle. In Figure 2, a similar comparison concerning the cyclic softening behavior is presented. While for the Chaboche model a stabilization is achieved the material is continuously softening in reality. The model parameters were chosen such that stress and strain amplitudes of the stabilized situation matched the measured values at half of the life for technical crack initiation. For the identification of the model parameters, an optimization algorithm described in reference [27] was applied. In general, the simulation accuracy was considered as sufficiently good.

7

Fig. 1: First loading and unloading at T = 20 °C and T = 180 °C, 42CrMo4

Fig. 2: Transient deformation behavior at T = 20 °C and T = 180 °C, εa = 0.02 (Rε = -1), 42CrMo4

A note is placed here that for the temperatures investigated, 20 °C ≤ T ≤ 180 °C, no influence was observable on the strain-life-curves while the sustainable stress amplitudes where up to 10 % lower for 180 °C than for 20 °C, for the same life to technical crack initiation.

3 Fatigue strength of intersecting hole specimens The test specimen, Figure 3, resembles the typical, critical geometric detail of injection components, intersecting holes. Specimens with and without autofrettage have been tested under cyclic internal pressure at the Materials Research and Testing Institute Weimar, see [5]. The autofrettage pressure – applied at room temperature – was 850 MPa. The main interest in the technical field of concern lies 8

on the endurance limit. The number of applied cycles of injection components is very high and therefore only pressure ranges sufficiently below the fatigue limit can guarantee safe operation of the engine for the required time of its operation. Nevertheless, the pressure-life-curve in the high cycle fatigue region was also determined in the present investigation.

Fig. 3: Geometry of the test specimen. The red lines mark one of eight symmetric sectors of the bottom half which is modeled as finite element mesh for numerical analysis

The close inspection of autofrettaged run-out specimens, Figure 4, revealed that all of them contained fatigue cracks which had initiated at the critical location, the notch at the intersection edge of two holes. According to the Theory of Elasticity the maximum principal notch stresses are a factor of 4.98 larger than the applied internal pressure. The growth of fatigue cracks starting at this location obviously ceases while entering further into the field of compressive residual stresses. A sound modelling of the process therefore requires knowledge of the residual stress field and application of an approach based on fracture mechanics.

9

a) Front view on intersection edge

b) Top view on fracture surface

Fig. 4: Fractography of run-out autofrettaged specimens showing a fatigue crack arrest in the field of compressive residual stresses after growth of approximately 2mm measured in bisector direction

3.1 Residual stress field Deformations and residual stresses were calculated applying finite element technology and the material model described in the previous section. From the observation of the fracture surfaces it was concluded that the condition on whether or not a crack may arrest is decided at the crack front at the bisector. Therefore, residual stress distributions are shown along the bisector in Figure 5.

a) Residual stress redistribution due to cyclic loading

b) Residual stress redistribution due to mechanical and temperature effect

Fig. 5: Residual stress distributions of autofrettaged specimens

10

The solid red lines in Figures 5a and 5b show the residual stresses immediately after application and removal of the autofrettage pressure of 850 MPa. The hoop stress, 33, is plotted where the local x3coordinate is oriented perpendicularly to the fracture plane (the latter shown in Figure 4b). The dotted red line in Figure 5b shows the residual stresses after heating the specimen to 180 °C without applying any internal pressure. Both Figures 5a and 5b further show – indicated by lines with various markers – the redistribution of residual stresses due to 251 operating pressure cycles. Various values of pmax and an always constant value of pmin = 5 MPa (in accordance to the experiments) were applied cycle by cycle. The hoop stress, 33, is plotted for the configuration loaded with pmin = 5 MPa – therefore, the stresses shown are not exactly but very close to the residual stresses. To indicate this, parentheses surround the word “residual” at the ordinates for Figures 5a and 5b.

The major effect observed is cyclic mean stress relaxation with a continuously decreasing the rate. Stopping these calculations after 251 cycles is a compromise between numerical expense and obtained accuracy which was already made in a previous investigation [4]. On the one hand (residual) stress redistribution has then become very slow and on the other hand crack nucleation is supposed to have occurred which is probable to contribute a larger and larger amount to further stress redistribution not captured by calculations for the uncracked configuration.

3.2 Fatigue crack growth A realistic assessment of the fatigue strength of the components under consideration requires the application of an approach based on fracture mechanics. Especially, fatigue crack growth in residual stress fields has to be modelled. Several approaches based on either linear elastic or elastic-plastic fracture mechanics have been applied in the present investigation. Simultaneously their potential to realistically describe the components’ fatigue behavior was evaluated. 11

3.2.1 Stress intensity factors Finite element models of the specimen with quarter-circular cracks at each hole intersection edge have been created varying the crack length between 0.01 mm and 10 mm. All symmetries have been exploited so that only one sixteenth of the structure had to be created. Finite element models for the bottom half of the 45° sector shown in Figure 3 as red lines have been created. The unit load cases “pressure on holes” (HO) and “pressure on crack flanks” (CF) as well as the residual stress case were investigated and the resulting stress intensity factors were gained by applying the method of virtual crack closure integral [28][29]. Only the stress intensity factors for the position where the crack front intersects with the bisector are considered here. The results are shown in Figure 6. Thus, the dimension of the problem is reduced to an assessment of the unidirectional growth of a single crack tip along the bisector line.

For easing fatigue crack growth calculations and for calculating stress intensity factors due to residual stresses it is convenient to have weight functions,

, at hand. The weight function method

allows for a quick calculation of stress intensity factors for arbitrary crack lengths and load situations. The weight function has to be multiplied with the stress distribution of the uncracked configuration at crack flank positions, x, and the product has to be (numerically) integrated over the crack length, . The known solution for the two unit load cases mentioned above enables the derivation of the weight function for the current specimen following the method of Shen and Glinka [30][31]. Expecting that the result obtained here can be used for similar configurations of intersecting holes the weight function is printed as Equation (8):

(8)

with 12

for mm

for

mm mm

for

mm

mm mm

mm

mm

(8a)

mm (8b)

for for

mm mm

(8c)

mm

The Figures 6a and 6b also show the comparison of stress intensity factors obtained directly from the finite element calculation and from the integration of the weight function. The solution for the unit load cases is described perfectly because the weight functions have been derived from the numerical solution of these load cases. For the residual stress case the approximation is extremely good for crack lengths smaller than 5 mm.

20

10

-1

K(

10

s) ole nh ao P 1M p=

-2

K(

p

Symbols: Finite element solution K in MPa m

K in MPa m

10

ks) an k fl rac c n ao MP =1

0

Lines: Weight function based solution

-10

-20

Symbols: Finite element solution Lines: Weight function based solution

0.01

0.1

1 a in mm

a) Unit load cases pressure (p=1 MPa) on

10

-30 0.01

0.10

1.00

a in mm

10.00

b) Due to residual stresses

holes and crack flanks Fig. 6: Stress intensity factors

3.2.2 Fatigue crack growth calculations based on linear elastic fracture mechanics In an approach based on linear elastic fracture mechanics the crack growth rate and the arrest condition are expressed in terms of the range of the stress intensity factor,

, defined here as 13

(9) with (10) and .

(11)

Figure 7 shows a typical graph of the stress intensity factor range for the specimen with residual stresses due to autofrettage. A minimum appears at crack lengths between 1 mm and 2 mm. If the operating pressure is low enough the minimum drops below the threshold,

, the crack arrest

condition is met and the specimen will not fail, see Figure 4. The corresponding pressure marks the specimen’s endurance limit, used, and

. For room temperature a threshold of

was

was assumed, the reduction ratio based on the ratio of yield

stresses at the corresponding temperatures. For higher pressures than the endurance limit, finite fatigue lives have been calculated by integrating a power-law-type rate equation,

(12)

between the limits of an assumed initial flaw size of

and a final crack length of

for which failure was defined. The exponent was set to are again temperature dependent, especially

and the parameters and

.

Results are shown in a later section together with experimental and more numerical results.

14

100 80 60

K in MPa m

40

p = 495MPa

= 395MPa

20

= 345MPa 10 8

= 321MPa Kth

6 4 0

1.0

2.0

3.0

a in mm Fig. 7: Range of stress intensity factors as function of the crack length for various maximum operating pressures and a minimum pressure of

, autofrettaged specimen, room temperature

The crucial assumption behind the modeling is that a crack can only grow under a positive stress intensity factor. Equation (9) can be interpreted such that a crack is supposed to close, i.e. its flanks get into contact, if

. The ranges with positive stress intensity are effective in growing the crack.

However, it is well known since Elber’s publication [32] that fatigue cracks open at load-proportional stress intensities considerably different from zero. The obvious model error encountered here is largely healed by applying empirical parameters, crack growth behavior observable for

and

, which adjust the model’s output to

loading.

15

3.2.3 Fatigue crack growth calculations based on the strip yield model Calculating realistic ranges for which the crack is open (and therefore can grow) requires taking cyclic elastic-plastic deformation into account. From this motivation, approaches based on elastic-plastic fracture mechanics have been applied. This increases the numerical expense considerably. The strip yield model is the less expensive of the approaches because it confines the plastic deformation in a narrow, in the end, infinitely thin strip around the crack-ligament line. The present application again restricts modeling to the bisector line which coincides with the x-coordinate in Figure 8. The crack length in this direction is again , the size of the plastic zone ahead of the physical crack tip is

. Bar

elements are arranged along the crack-ligament line (x-axis) which are allowed to deform in a rigidplastic way if the local stresses reach the yield stress (in tension or compression). The deformation behavior of the surrounding structure is linear elastic. Plastically elongated bar elements remain at the crack flanks as the physical crack tip moves along the x-axis (i.e. the crack grows). Their contact defines plasticity induced crack closure. The plastic deformation at the physical crack tip – the range of the crack tip opening displacement,

, is assumed to act as crack driving force according to an

empirical power law,

.

The parameters are

(13)

and

. A threshold condition was also introduced as

and all parameters are supposed to be independent of temperature, according to a proposal of Schmidt et al. [33].

16

Physical crack tip

y

Fictitious crack tip

x1

xr



a

xn

x

y

li xi

vi /2

xj x

b 1, j b2, j

i d

Fig. 8: Strip yield model

Modeling and encoding the algorithm as a software package followed the description of several authors [34][35][36]. Required input consists first of all of the stress intensity factor solution as provided in the previous section. Additionally, the crack flank displacements,

, have to be

supplied in a convenient format. Wang and Blom have shown in [37] how this can be achieved by also using weight functions, originally reading as (14)

.

(15)

The variables are explained in Figure 8.

The three-dimensional problem of quarter-circular cracks at the hole intersection edge is reduced to a two-dimensional problem formulated in the bisector plane. Comparisons of crack flank displacements calculated with Equations (14) and (15) with displacements obtained by finite element solution of the three-dimensional problem revealed that a modification of Equation (15) was

17

necessary to be introduced: a different weight function second call of

had to be determined replacing the

in Equation (15) and leading to

(16)

with

(17)

and

mm

(18a)

mm

mm

(18b)

mm for mm

mm

(18c)

mm

(18d)

mm

(18e)

mm

for

mm

mm

mm

mm

(18f)

(18g)

18

(18h)

mm

mm

mm

mm

mm

mm

(18i)

For introducing the residual stresses in the strip yield model, the bar elements, Figure 8, receive an initial length, , via an input. These lengths are calculated according to the condition that the resulting residual stresses deliver the same stress intensity factors as the residual stresses in the component (for identical crack lengths). The details of the algorithm are explained in reference [2].

A further extension of the strip yield model concerns consideration of temperature. The temperature can be defined individually for each bar element and together with temperature an individual yield stress may be attached to each bar element. More details are provided in references [38] and [39].

A final model extension was implemented concerning the reproduction of the material’s non-linear elastic-plastic deformation behavior. Usually, the strip yield model works with a constant yield stress. The ligament’s deformation behavior is rigid plastic. Here, individual bar elements are equipped with individual yield stresses. Although each bar element still behaves rigid-plastically, the parallel array of these elements deforms according to a polygonal stress-strain curve. An array was chosen here such that the cyclically stabilized stress-strain-curve of the present material, 42CrMo4, was represented. Along the crack-ligament line the yield stresses were randomly speckled. Additionally, bar elements with very high yield stresses adjacent to the crack initiation position have been replaced by bar elements with lower yield stresses. A couple of realizations were investigated each leading to a different fatigue strength. Thus, an estimate of scatter in fatigue lives was obtained. More details are explained in reference [40]. 19

Figure 9 shows the course of the crack driving force,

, with crack length. Several minima are

observed for crack lengths between 0.3 mm and 1 mm which occur whenever the crack tip approaches a bar element with a high individual yield stress. If the crack driving force drops below the threshold, crack arrest or endurance limit, respectively, is predicted. Further results are shown in a later section together with experimentally and more numerically obtained results.

10

2. 10 10

p = 300MPa, RT

-3

 in mm

10

p = 255MPa, RT

-4

-5

th

-5

0.1

0.2

0.4

0.6 a in mm

0.8 1.0

2.0

Fig. 9: Range of crack tip opening displacement as function of the crack length for and

, respectively,

, autofrettaged specimen

3.2.4 Finite element based crack growth simulations The reduction of the geometry to a two-dimensional plane and the restriction with elastic-ideally plastic material behavior, although with individual and temperature dependent yield stresses, are still a severe simplifications of reality. The determination of the residual stresses has already been performed using a three-dimensional mechanical model together with a powerful material model, 20

see section 2. In an attempt to overcome the simplifications, fatigue crack growth simulations have been executed, based on the finite element (FE) technology in combination with a node release scheme described in the following.

The present symmetric geometry and the symmetric boundary condition allow a reduction of the overall model to a 1/16 symmetry model, which was used exclusively in the FE-simulation. A casestudy of various FE-calculations was performed using hexahedral elements with linear shape functions and reduced as well as full integration in order to gain a detailed understanding of the cyclic plasticity behavior. In Fig. 10, the model definitions with temperature influence starting from an autofrettage pressure of 850 MPa at 20 °C and subsequent cyclic operating pressure load with about 250 cycles at 180 °C can be seen.

Fig. 10: Finite element model, boundary conditions and load scheme

Prior studies [4] have noted the importance of applying about 250 load cycles after the initial autofrettage cycle as a recommendation to adequately describe the inherent stress redistribution due to cyclic loading. The crack propagation simulation is then carried out with the node release 21

technique, which is defined after 10 load cycles by opening the boundary conditions until the next crack front, while the crack surface is loaded. Fracture mechanics based studies at room temperature using a novel crack propagation technique as a mapping method are presented in [41][42][43]. Based on this preliminary works, the focus in this chapter is on the additional inclusion of the influence of temperature and elastic-plastic fracture mechanics on the fatigue strength of autofrettaged components. An extension of the J-integral to cyclic loads is presented by Dowling and Begley in [44] (19) (20) where

, ∆ti, ∆εij and ∆ui are the changes in the Cauchy stress tensor, stress vector, strain tensor

and displacements relative to a reference state and can be interpreted as cyclic ranges. In contrast to this, the values ΔW and ΔJ do not represent cyclic ranges, but they could be treated as absolute values. Taking in account the crack-closure effect, the use of the cyclically effective J-integral is recommended. The ΔJeff value is determined on the unloading branch with the limits in the upper load reversal point (reference state) and the state of the crack closing, which is determined by an algorithm. Furthermore this algorithm enables detailed statements about the crack-opening and crack-closing properties, characterized by the determination of the times and pressures at crackopening and closing. The crack propagation simulation with the finite element method, taking into account the plastic deformation behavior, was carried out with a predetermined crack surface geometry and an empirically determined crack initiation length of a0 = 0.2 mm. The closure pressure values are slightly smaller than the corresponding opening pressure values. An important aspect of the temperature influence is its impact on the closure and opening pressures as shown in Fig. 11. For higher temperatures the effective pressure ranges increase.

22

Fig. 11: Crack opening and closure pressure; influence of temperature

During an iterative procedure, the external cyclic load is varied until the defined state of this fatigue strength definition is reached. In other words, the crack growth stops if the calculated ∆Jeff-value touches or decreases below the ∆Jeff -threshold curve representing the endurance limit at a certain pressure range. Graphs of the ΔJeff -values as function of the crack length are shown in Figure 12 for various applied maximum pressures. The ΔJeff -threshold values of ∆Jeff, th, T20 = 0.041 N/mm at T = 20 °C and ∆Jeff,th, T180 = 0.037 N/mm at T = 180 °C, see Fig. 12, have been applied. According to the results of the elastic-plastic FE-analysis the endurance limit at T = 20 °C is defined by ∆pE, T20, Sim = (302 – 5) MPa = 297 MPa and at T = 180 °C a value of ∆pE, T180 Sim = (262 – 5) bar = 257 MPa appears.

23

a) At room temperature

b) At 180 °C

Fig. 12: Effective cyclic J-integral as function of the crack length for various maximum operating pressures and a minimum pressure of

, autofrettaged specimens

4 Comparison of numerical and experimental results For Diesel engine injection components, the endurance limit is the most important information on their fatigue behavior. Experimentally and numerically determined endurance limits for a probability of exceedance of 50 % are compared in Figure 13. The numerical, fracture mechanics based approaches are specialized to realistically consider for the crack arrest occurring in autofrettaged intersecting holes. For non-autofrettaged specimens, the endurance limit is determined by a crack initiation condition. If a technical crack initiates in the highest stressed location at the intersection edge, the specimen will fail. A local strain approach will serve best to assess the endurance limit of non-autofrettaged specimens. Against the background of this insight, the two simpler of the fracture mechanics based approaches have been applied for fatigue strength calculation of the nonautofrettaged specimens. In the linear elastic fracture mechanics (LEFM) based approach the level of the endurance limit is strongly related to the assumed initial flaw size in combination with the threshold value for 24

loading. The threshold of

is well known whereas the initial flaw size of

is assumed such that a realistic endurance limit is obtained. For the autofrettaged specimens, the initial flaw size is less important due to the decisive phenomenon of crack arrest after fatigue crack growth has already occurred. It turns out that the approach overestimates the effect of compressive residual stresses by approximately 20 %. The effect of temperature – reduction of the endurance limit up to 10 % at 180 °C – is underestimated. A variety of model modifications (with respect to geometry, estimation of effective ranges or material strength parameters) can be imagined to improve the situation, however, considering elastic-plastic deformation behavior was

operating pressure range endurance limit in MPa

regarded as most promising.

400

Experiment linear elastic fracture mechanics (LEFM) strip yield model (SYM) finite element based crack growth simulation (FE)

300

200

100

0 not autofrettaged room temperature

not autofrettaged 180°C

autofrettaged room temperature

autofrettaged 180°C

Fig. 13: Comparison of experimentally and numerically determined endurance limits for a probability of exceedance of 50 %

The initial flaw size of

has been chosen in the strip yield model (SYM). Due to the

replacement of bar elements with very high yield stresses in the region of crack initiation by weaker 25

bar elements, the crack driving force,

, first decreases with crack length. The endurance limit of

non-autofrettaged specimens is determined by microstructural barriers appearing as high yield stress bar elements ahead of the growing crack. The endurance depends on the very realization of the random microstructure. As is shown in Figure 13, the chosen distributions of bar elements’ yield stresses produce realistic results for not autofrettaged specimens. The effect of the compressive residual stress fields in autofrettaged specimens is underestimated by approximately 10 %. The temperature influence is taken into account realistically.

The finite element based crack growth simulations in connection with the cyclic effective J-integral provided best accuracy for the autofrettaged specimens. An overestimation of the endurance limit of 5 % was observed, the temperature influence was captured in a nearly perfect way. The application of this method to non-autofrettaged specimens was set aside. The extremely high expense is not considered to be justified by the result which can be expected and which will be similar to the results of the previously discussed approaches. The crucial fitting parameter again would be the equivalent initial flaw size.

In Figure 14 the pressure life curves are compared. The experimental results appear as circles, thin lines represent results obtained by applying the linear elastic fracture mechanics (LEFM) based approach, the thick arrows indicate the endurance limit level predicted by the finite element (FE) simulation, the strip yield model (SYM) provided several individual results shown as crosses. The scatter bands enclosing the individual results are drawn as hatched areas. The tendencies of underand over-estimation of the fatigue strength as already discussed for the endurance limit can be seen in the finite life regime in a similar magnitude.

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500

range of operating pressure p in MPa

SYM

LEFM

400 LEFM 300

3

FE-Sim.

SYM

8 7

autofrettaged

200

not autofrettaged 6 6

blue: room temperature red : 180°C circles : experimental results crosses : strip yield model results 100 4 10

5

6

10 10 10 number of applied operating pressure cycles until leakage, N

7

Fig. 14: Life curves for intersecting hole specimens of 42CrMo4.

5 Recommendations and conclusions As far as the influence of temperature is concerned, nearly all strength parameters and characteristic functions lose approximately 5 % to 10 % of their room temperature values if the temperature rises to 180 °C. For practical purposes, it can be recommended to determine the fatigue strength for room temperature environment and to reduce the result by 10 %. The endurance limits of specimens which have not been autofrettaged even slightly increases with temperature. On a first glance, this result is surprising. However, it can be explained by observing the local notch root hysteresis loop at the endurance limit level. For both temperatures, only very small plastic strain amplitudes appear. With respect to the amplitudes, the loops are practically identical. Due to the lower yield stress of the material at 180 °C the corresponding loop reveals a lower maximum and also a lower mean stress. This effect is supposed to explain the observation. The strip yield model is able to take this effect into account – shown as crossing

-curves in Figure 14.

Approaches only based on linear elasticity are condemned to lose this influence. 27

The current application of autofrettaged intersecting holes loaded by cyclic internal pressure is tightknit with the phenomenon of crack arrest at the endurance limit. For less sharply notched components the endurance limit is determined by the local stresses and strains at the critical crack initiation location. The information whether or not crack arrest plays a role in a given design requires the application of a fracture mechanics based approach. Otherwise a large amount of the component’s fatigue strength may be under-utilized – an option not available in today’s commercial and competitive world. The fracture mechanics based approaches are able to cope with the crack initiation phenomenon, see Figure 14. A prerequisite is the determination of the initial, probably micro-structurally short initial flaw size. Either this initial flaw size is gained by fitting calculation to experimental results (LEFM-approach), or models considering microstructural issues and crack length dependent crack closure are used (SYM-approach). In the latter case it can be shown that classical local strain approaches and fracture mechanics based approaches are equivalent. Reference [45] provides a more detailed discussion of this ambivalence.

Fracture mechanics based assessments of the fatigue strength may be performed at various levels of complexity and realism. The approaches have in common that a realistic distribution of residual stresses in the plane of fatigue crack growth must be determined first. Powerful plasticity models as well as computer resources are available today. A comparison of numerically obtained with measured residual stress fields is needed – a task for future research.

The approaches applied here yield more accurate results with an increasing level of realism, however, an even stronger increasing numerical expense must be paid. The responsible engineer must find his own optimum. Hopefully, the results presented in this paper are helpful.

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Acknowledgement The authors gratefully acknowledge funding by the German Bundesministerium für Wirtschaft und Energie (BMWi) provided via the Arbeitsgemeinschaft industrieller Forschungsvereinigungen „Otto von Guericke“ e.V. (AIF) for the research project „Temperature and high pressure“, supported by the Forschungsvereinigung Verbrennungskraftmaschinen e. V. (FVV) under grant IGF-Nr. 17987 BG. Special thanks go to the members of the research team at the Materialforschungs- und -prüfanstalt (MFPA) at the Bauhaus-Universität-Weimar for scientific exchange and cooperation during the common project.

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Highlights

    

Autofrettage increases fatigue strength of sharp notches by a factor of 2 or more Elevated temperature influence has been investigated for the first time At 180°C the fatigue strength decreases by 10% compared to room temperature At all temperatures the fatigue limit is determined by the arrest of fatigue cracks Good predictions are achieved by fracture mechanics based modeling approaches

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