11.3Fundamentals of Fracture Control and Fracture Mechanics

Titanium fasteners

Over the years, a lot of debate has occurred about the risks associated with the application of titanium preloaded fasteners. The latest NASA fracture control standard [ref 11.16] prohibits titanium for low risk fasteners, while for fracture critical and safe life fasteners titanium is discouraged (esp. for fracture critical ones) and subject to approval of the responsible fracture control authority. The ECSS standard [Ref 11.1] prohibits titanium safe life fasteners generally, but defines no specific limitation for fail-safe titanium fasteners.

The concerns highlighted in NASA-STD-5019A are: generic environmentally assisted or sustained load cracking failure modes, as well as low fracture toughness. For safe life (damage tolerant) titanium fasteners: Titanium alloys, such as Ti-6Al-4V (including annealed and STA conditions), cp-Ti, and other titanium alloys, have potential generic EAC or SLC failure modes that are to be addressed in the assessment with test data from flawed fasteners in the applicable service life environments (incl. air).

Additional background information on sustained load cracking of titanium can be found in Ref. [11.17].

In addition, NASA-STD-5019A explains: Growth of a pre-existing crack in susceptible metallic alloys under sustained stress without assistance from an external environment. SLC, because of the presence

of interstitial hydrogen, occurs in titanium alloys, including commercially pure titanium (cp-Ti) and Ti- 6Al-4V (Ti64), in both annealed and solution treated and aged (STA) conditions. Testing is necessary to determine the threshold stress intensity for the titanium alloy metallurgical condition and interstitial hydrogen content. Other materials with different crystalline structures such as steel and aluminum alloys that do not allow interstitial hydrogen can still exhibit SLC behaviours. A threshold stress intensity factor can be obtained by procedures such as those in ASTM E1681 for the case of an inert or vacuum environment. One publication determines the effects of hydrogen content and temperature on SLC in Ti-6Al-4V (Boyer and Spurr, 1978, Ref. [11.18]).

An update of the ECSS fracture control standard was released in 2021 (Rev. 2 of Ref. [11.1]). For uncrewed application titanium safe life fasteners are now permitted, based on a sustained load cracking threshold of 50% of the fracture toughness. This 50% value is considered a reasonable lower bound of the values observed in literature (Ref. [11.17] and specifically [11.19] and [11.20]).

For more critical applications (esp. human spaceflight), additional test data can be required for verification.

As part of the so-called ‘reduced fracture control programme’ (applicable to non-human spaceflight) a new risk-based approach for safe life fasteners is included, based on the fact that a crack of the order of 0,63mm (a value of 0,025” used also in some NASA standards) can be considered as unlikely to exist in a high-quality part, independent of the applied NDI. Note that for critical applications a larger initial crack size can apply. In Figure 11-13 to Figure 11-18 some residual bolt strength curves are presented for some commonly applied fastener materials, which provide rough indications of the maximum sustained stress level allowed in the fasteners in the limiting case that no significant fatigue crack growth occurs. The curves are defined using the NASGRO (v.9) model SC08 (see also Figure 11-20) with crack size a=c=0,63mm. The red lower bound curves is defined by the minimum strength defined by toughness (K1e or 50% of K1e for titanium; blue curves) and flow stress (average of yield and ultimate strength; orange curves). In most cases, the flow stress criterion is driving, except for Ti6Al4V STA (Figure 11-13). The toughness curve tends to be slightly decreasing for increasing bolt size, because the larger root radius causes an increased depth affected by high stresses (size effect of stress concentration). The curve based on the flow stress criterion tends to be slightly increasing, due to the relative decrease of the crack size w.r.t. the cross-sectional area. For reference, lines at applied sustained stress levels 70% (yellow), 80% (blue) and 90% (green) of the yield strength (for uncracked geometry) are also provided.

Internal thread in safe life items can be of particular concern, because it will be difficult to inspect and cracks could emanate from sharp notches, and only few suitable standard cracked geometries exist in crack-growth software like NASGRO. It is recommendable to avoid this wherever possible. Such threads will not only be directly loaded by the bolt, but can also be loaded by other loads applied to the item, and the resulting stress distribution can be complex. This can be the most critical location of the part, even if the corresponding bolt pattern is verified as fail safe. The acceptance rationale can also benefit from the risk-based approach, using 0.63mm initial crack size, mentioned above (see ref. 11.1, rev.2, clause 11.2.2.6), at least for non-human spaceflight. In some cases also the a so-called ‘maximum machining defect’ (of depth 0,127mm all along the thread), mentioned above for external thread, can be considered as additional risk assessment.

Figure description:

Allowable stress for STA Ti6Al4V bolts

Allowable stress, STA Ti6Al4V, 0.5K1e (955.5MPa√mm and Sflow (1110MPa , a=c=0.63mm

Legend

• Sall,K — color: blue; symbol: Solid line with circle markers
• Sall,Sflow — color: orange; symbol: Solid line with circle markers
• Sall,envelope — color: red; symbol: Solid line with grey circle markers
• 0.7xYS — color: yellow; symbol: Dashed line with circle markers
• 0.8xYS — color: dark blue; symbol: Dash-dotted line with circle markers
• 0.9xYS — color: green; symbol: Dash-dotted line with circle markers

YS=1070MPa; K1e =1910MPa√mm; sustained stress limited by 0.5x K1e

Figure 11-13 – Residual bolt strength under sustained loads, Ti6Al4V STA

Figure description:

Allowable stress, annealed Ti6Al4V, 0.5K1e (1129.5MPaVmm and Sflow (978.5MPa , a=c=0.63mm

Allowable stress, annealed Ti6Al4V, 0.5K1e (1129.5MPaVmm and Sflow (978.5MPa , a=c=0.63mm

Legend

• Sall,K — color: light blue; symbol: Solid line with circles
• Sall,Sflow — color: orange; symbol: Solid line with circles
• Sall,envelope — color: red; symbol: Thick solid line with grey circles
• 0.7xYS — color: yellow; symbol: Dashed line with circles
• 0.8xYS — color: dark blue; symbol: Dashed line with circles
• 0.9xYS — color: green; symbol: Dashed line with circles

YS=950MPa; K1e =2260MPa√mm; sustained stress limited by 0.5x K1e

Figure 11-14 – Residual bolt strength under sustained loads, Ti6Al4V annealed

Figure description:

Allowable stress, A286, K1e (4865MPa∘mm and Sflow (962.5MPa , a=c=0.63mm

Allowable stress, A286, K1e (4865MPa∘mm and Sflow (962.5MPa , a=c=0.63mm

Legend

• Sall,K — color: Light blue; symbol: Line with circle
• Sall,Sflow — color: Orange; symbol: Line with circle
• Sall,envelope — color: Red; symbol: Solid line with circle
• 0.7xYS — color: Yellow; symbol: Dashed line with circle
• 0.8xYS — color: Blue; symbol: Dashed line with circle
• 0.9xYS — color: Green; symbol: Dashed line with circle

YS=825MPa; K_1e=4865MPa√mm

Figure 11-15 – Residual bolt strength under sustained loads, A286 steel

Figure description:

Allowable stress, Inconel 718, K1e (2432MPa√mm and Sflow (1482.5MPa , a=c=0.63mm

Allowable stress, Inconel 718, K1e (2432MPa√mm and Sflow (1482.5MPa , a=c=0.63mm

Legend

• Sall,K — color: light blue; symbol: line with circle markers
• Sall,Sflow — color: orange; symbol: line with circle markers
• Sall,envelope — color: red; symbol: thick solid line
• 0.7xYS — color: yellow; symbol: dashed line with circle markers
• 0.8xYS — color: dark blue; symbol: dash-dotted line with circle markers
• 0.9xYS — color: green; symbol: dash-dotted line with circle markers

YS=1415MPa; K_1e=2430MPa√mm

Figure 11-16 – Residual bolt strength under sustained loads, Inconel 718

Figure description:

Figure 11-17

• Title: Residual bolt strength under sustained loads, AISI 316 stainless steel
• Material Properties: YS = 690 MPa; $K_{IE}$ = 4345 MPa$\sqrt{mm}$
• X-axis: Crack depth 'a' [mm, range 0 to 6
• Y-axis: Residual Strength [MPa, range 0 to 800
• Key Entities (Bolt Sizes: M2.5, M3, M4, M5, M6, M8

Figure 11-18

• Title: Residual bolt strength under sustained loads, MP35N STA
• Material Properties: YS = 1750 MPa; $K_{IE}$ = 3650 MPa$\sqrt{mm}$
• X-axis: Crack depth 'a' [mm, range 0 to 6
• Y-axis: Residual Strength [MPa, range 0 to 2000
• Key Entities (Bolt Sizes: M2.5, M3, M4, M5, M6, M8

Figure description:

Allowable stress for various thread sizes AISI 316, 20% CW, K1e (4344MPaVmm and Sflow (725MPa , a=c=0.63mm

Allowable stress, AISI 316, 20% CW, K1e (4344MPaVmm and Sflow (725MPa , a=c=0.63mm

Legend

• Sall,K — color: light blue; symbol: solid line with circles
• Sall,Sflow — color: orange; symbol: solid line with circles
• Sall,envelope — color: red; symbol: solid line with grey circles
• 0.7xYS — color: yellow; symbol: dashed line with circles
• 0.8xYS — color: blue; symbol: dashed line with circles
• 0.9xYS — color: green; symbol: dashed line with circles

YS=690MPa; K_1e=4345MPa√mm

Figure 11-17 – Residual bolt strength under sustained loads, AISI 316 stainless steel

Figure description:

Allowable stress, MP35N STA, K1e (3649MPaVmm and Sflow (1820MPa , a=c=0.63mm

Allowable stress, MP35N STA, K1e (3649MPaVmm and Sflow (1820MPa , a=c=0.63mm

Legend

• Sall,K — color: light blue; symbol: Solid line with circle
• Sall,Sflow — color: orange; symbol: Solid line with circle
• Sall,envelope — color: red; symbol: Solid line (with gray circle markers in plot
• 0.7xYS — color: yellow; symbol: Dashed line with circle
• 0.8xYS — color: blue; symbol: Dashed line with circle
• 0.9xYS — color: green; symbol: Dashed line with circle

YS=1750MPa; K_1e=3650MPa√mm

Figure 11-18 – Residual bolt strength under sustained loads, MP35N STA

11.3.3.1 Overview

This section is based on an older version of the NASGRO software (Ref. [11.3] or [11.4]) as well as other literature and will not be fully up to date with the latest NASGRO version (Ref. [11.9]). Cracked fastener models are still being further developed.

In a fastener subjected to both tensile and bending loads the correction factor for stress intensity factor is calculated by,

where $\sigma_{0}$ and $\sigma_{1}$ are the tensile and bending components of the normal stress at the crack location (see Section 11.3.3.2 below), and, $F_{0}$ and $F_{1}$ are that amplification factors specific to the tensile and bending stress fields respectively.

The following three types of cracks are most likely to occur in fasteners:

circumferential crack at the thread (most likely in fasteners with cut threads),

thumbnail crack at the thread (most likely in fasteners with rolled threads loaded in bending), and thumbnail cracks at the fillet under the fastener head

The ESACRACK/NASGRO software calculates stress intensity factors for these and other crack types, including those mentioned in this section. The following sections briefly describe the theory adopted by ESACRACK/NASGRO.

11.3.3.2 Components of Local Stress

In Equation [11.3.2] the tensile and bending components of the local bending stress at the crack are given by,

and,

where Fb is the tensile force in the fastener, Mb is the bending moment in the fastener, and dlocal is the assumed local diameter of the fastener at the crack location, which is either:

• • d for circumferential cracks, or
• • $d_{3}$ for thumbnail cracks

11.3.3.3 Circumferential Cracks around the Thread

Figure 11-19 shows the assumed stress distributions (left) and geometry (right) of the ESACRACK/NASGRO model for circumferential fastener cracks.

Figure description:

Title: SC09

Visual Entities:

• Top Left Diagram: Side view of a threaded fastener in a material, labeled with tensile stress $\sigma_0$ and bending moment $M$.
• Bottom Left Diagram: Cross-section of the fastener showing:
  • $d$: Major diameter.
  • $h$: Thread depth.
  • $a$: Dimension encompassing the thread and crack.
  • "crack": Pointed to a circumferential line around the core.
• Top Right Diagram: Side view of a threaded fastener engaged with a "nut," labeled with stress $\sigma_1$ and bending moment $M$.

Variables and Definitions:

• $d$ = Major diameter
• $h$ = Thread depth
• $a = d + \text{crack depth}$
• $\sigma_0$ and $\sigma_1$ are based on $d$

Formula:

Damaged Out Thread

Figure 11-19 - ESACRACK Model of a Circumferential Crack

The following equations are used by ESACRACK/NASGRO to determine the stress intensity correction factors for circumferential cracks in the fastener thread:

where; $G_{o} = 0,5 + 0,25 k + 0,1875 k^{2} - 0,1815 k^{3} + 0,3655 k^{4}$, $k = 1 - 2 a/d$, And,

[11.3.6]

where;

11.3.3.4 Thumbnail Cracks at the Thread Root

Figure 11-20 shows the assumed stress distributions (left) and geometry (right) of the ESACRACK/NASGRO model for thumbnail fastener cracks.

Figure description:

• Header: SC08
• Diagrams:
  • Left image: A fastener with a "crack" at the thread root, subject to uniform stress $\sigma_0$.
  • Right image: A fastener and "nut" assembly with a crack, subject to bending stress $\sigma_1$.
  • Bottom center cross-section: Shows geometric parameters $a$ (crack depth, $2c$ (crack arc length, $d$ (major diameter, and $d_3$.
• Geometric Definitions:
  • $d = \text{Major diameter}$
  • $h = \text{Thread depth}$
  • $a = \text{Crack depth}$
  • $2c = \text{Crack arc length}$
  • $a/c = 1.0$
• Equations and Relationships:
  • $\sigma_0$ and $\sigma_1$ are based on $d$.
  • $\sigma_1 = \frac{32M_b}{\pi d^3}$

Rolled threads - Crack at first contact thread

Figure 11-20 - ESACRACK Model of a Thumbnail Crack

For this type of crack, the stress intensity correction factors for tension (F 0) and bending (F 1) are shown in Table 11-1 (from Reference 11.3).

Figure description:

Entities:

• Bolt Head: The upper horizontal component.
• Shank: The vertical cylindrical component below the head.
• Fillet: The curved transition region between the bolt head and the shank.
• Crack: A semi-elliptical "thumbnail" flaw located at the fillet.

Geometric Parameters:

• d: Shank diameter.
• D: Bolt head diameter.
• R: Fillet radius.
• a: Depth of the crack.
• c: Half-length of the crack along the surface.
• $\sigma$: Applied tensile stress acting vertically on the shank.

Key Visual Details:

• The diagram illustrates a cross-section of a tension bolt with a crack originating at the fillet radius $R$.
• Dimensions $d$, $D$, and $R$ define the bolt geometry.
• Dimensions $a$ and $c$ define the crack size and shape.
• Tensile loading is indicated by the $\sigma$ vectors.

For $a/d = 0,05$ it is important to use interpolation.

For the case of no crack (i.e. $a/d = 0$) the stress intensity correction factor is determined by the stress concentration factor $K_{t}$, which can be interpolated from Table 11-2, and an extra factor, $f_{x}$, which is given by,

11.3.3.5 Thumbnail Crack at Fillet Under Fastener Head

Figure 11-21 shows this type of crack.

SC14

Figure description:

Entities

• Fastener: A bolt with a splined head and a cylindrical shank.
• Fillet Crack: A crack located at the junction (fillet between the bolt head and shank.
• Substrate: The material through which the bolt passes.
• Cross-section: A circular view of the bolt shank showing the thumbnail crack geometry.

Key Parameters and Geometry

• Fillet Radius ($r$: $r = .1D$
• Tensile Stress: Indicated by $\sigma_0$ and downward arrows.
• Crack Depth: $a$
• Shaft Diameter: $d$
• Crack Width: $2c$
• Geometric Constraint: $a \le 0.5d$

Crack Aspect Ratios ($a/c$

• Rolled Fillet: $a/c = 1.0$
• Machined Fillet: $a/c = 0.645$

Tension Bolt - Crack in Bolt Head Fillet

The stress intensity factors for this type of crack are calculated as for a thumbnail crack at the thread root in Section 11.3.3.4 above except the following additional assumptions are made:

• • For a machined fillet a/c = 0,645
• • For a rolled fillet a/c = 1,0
• • r/d = 0,1
• • For a/d = 0 the stress concentration factor of 2,78 is used
• • For a/d = 0,05 smooth interpolation is used