The Fracture Mechanics calculator allows for fracture analysis of a cracked part. The methods used include Linear Elastic Fracture Mechanics (LEFM), the Failure Assessment Diagram (FAD), and residual strength analysis. See the instructions within the documentation for more details on performing this analysis. See the reference section for details on the methodology and the equations used.

Inputs

Input the details for the fracture analysis and hit 'Submit' to calculate results:

Geometry Inputs

Crack Type:

Reference

Width, b:

Thickness, t:

Through crack in center of plate

Material Inputs

Applied Stresses

Tensile Stress, σ_tens:

Bending Stress, σ_bnd:

Display Units

Display results in:

Custom (Edit)

Results

The results of the fracture analysis are detailed below. Refer to the fracture mechanics reference section for details on how these results were derived.

Results Summary Properties LEFM FAD Residual Strength

Results Summary

Summary tables of results are shown below. These tables give the factors of safety for the for the various analytical methods employed. Any factors of safety of at least 1 are shown in green, and below 1 are shown in red. It is the responsibility of the engineer to determine the appropriate factor of safety to use in design.

Linear Elastic Fracture Mechanics (LEFM)

The Factors of Safety (FS) for Linear Elastic Fracture Mechanics (LEFM) are given in the table below:

FS at a-tip	FS_LEFM.a
FS at c-tip	FS_LEFM.c

Failure Assessment Diagram (FAD)

The Factor of Safety (FS) for the Failure Assessment Diagram (FAD) is given in the table below:

FS for FAD

FS_FAD

Residual Strength

The Factors of Safety (FS) for Residual Strength are given in the table below:

FS on critical stress	FS_RSC.a
FS on critical crack length	FS_RSC.σ

See full result details on the other tabs (above).

Properties & Inputs

This section details the crack geometry, material properties, and applied stresses.

Applied Stress

σ_t	=		applied tensile stress
σ_b	=		applied bending stress

Crack Geometry

Crack Type:

a	=
c	=
b	=
t	=

Material Properties

(Material Properties)

Material:

S_ty	=	yield strength
S_tu	=	ultimate strength
E	=	elastic modulus
eL	=	percent elongation

K_1C	=	plane-strain fracture toughness

Flaw Tolerance Curve

Cannot calculate Flaw Tolerance Curve. Must specify a Percent Elongation value for material.

NAVSEA's Fracture Toughness Review Process (FTRP) defines a minimum material that is deemed to be fracture safe. The FTRP also defines a means of calculating a flaw tolerance curve for a material, which is an indication of the material's resistance to fracture. For a material to be considered fracture resistant, it must have a flaw tolerance curve above that of the minimum material curve.

Linear Elastic Fracture Mechanics (LEFM)

The Factors of Safety (FS) for Linear Elastic Fracture Mechanics (LEFM) are given below. Full detailed calculations are provided in the following sections.

FS at a-tip	FS_LEFM.a
FS at c-tip	FS_LEFM.c

Overview

The stress intensity factor, K, is calculated and compared to the critical stress intensity (i.e. the fracture toughness), K_crit. The stress intensity is calculated as:

where σ is the applied stress, a is the crack length, and Y is a dimensionless geometry factor that is dependent on the crack and part geometry.

Fracture Toughness vs. Thickness

The fracture toughness is dependent on part thickness. As the thickness increases the fracture toughness decreases until the plane-strain fracture toughness, K_1C.

The fracture toughness (i.e. critical stress intensity) values for the plane-strain condition and for the current part thickness are provided in the table below:

Plane-Strain Fracture Toughness	K_1C =
Fracture Toughness at Part Thickness	K_c =

For this analysis, we have elected to use the :

K_crit =

fracture toughness considered in this analysis

Geometry Factor

The plot below shows the dimensionless geometry factors as a function of crack length.

It is important to note that in the plot, the proportions of the crack dimensions a and c are held constant as the crack is grown. This is a simplified approximation. If crack growth due to cyclic loading is a concern, then a fatigue crack growth analysis should be performed.

The table below provides the geometry factors for tension in bending at the a-tip and the c-tip:

	a-tip	c-tip	Description
Y_t			geometry factor for tension at a-tip and c-tip
Y_b			geometry factor for bending at a-tip and c-tip

Stress Intensity

The stress intensity factors at the a-tip and the c-tip are:

At a-tip:
At c-tip:

Reference Values

a	=
c	=

σ_t	=
σ_b	=

The Factors of Safety (FS) on LEFM at the a-tip and the c-tip are:

At a-tip:

At c-tip:

Reference Values

K_crit	=

K_app.a	=
K_app.c	=

Plastic Zone Size

Plane-Stress vs. Plane-Strain

The size of the plastic zone is dependent on whether the part is considered to be in a plane-stress or a plane-strain condition. The minimum thickness for the part to be in plane-strain is:

Reference Values

K_app.max	=
S_ty	=

The actual part thickness of is than the minimum plane-strain thickness, so the part is considered to be in the condition.

Plastic Zone Size

The equation for the plastic zone size is dependent on whether the part is considered to be in plane-stress or plane-strain:

Variable	Equation
Plastic zone size for plane-stress:
Plastic zone size for plane-strain:

This part is in plane-strain, so the plastic zone size is:

This part is in plane-stress, so the plastic zone size is:

Applicability of LEFM

For LEFM to be applicable, the plastic zone size must be small relative to the part and crack geometry. The plastic zone is situated just ahead of the crack tip. In general, the tip of the crack must be a distance of at least d_LEFM from any part boundary, where d_LEFM is defined below:

Reference Values

K_app.max	=
S_ty	=

The value of d_bound is than the distance d_LEFM, so .

Failure Assessment Diagram (FAD)

Cannot calculate FAD results. Must specify a Percent Elongation value for material.

The Factor of Safety (FS) for the Failure Assessment Diagram (FAD) is given below. Full detailed calculations are provided in the following section.

FS for FAD

FS_FAD

The Failure Assessment Diagram (FAD) accounts for both elastic and plastic material behavior. The material behavior is defined by the stress ratio, S_r, and the stress intensity ratio, K_r.

The ratios for the current case are:

Stress Ratio:
Stress Intensity Ratio:

Reference Values

σ_cmb	=
K_app	=

S_ty	=
K_1C	=

The critical stress ratio and stress intensity ratio are the ratios at which failure occurs, and occur when the load line in the FAD diagram intersects the failure locus:

Critical Stress Ratio:	S_r.crit =
Critical Stress Intensity Ratio:	K_r.crit =

The critical stress, σ_crit, and the critical stress intensity, K_crit, are the σ and K values at which failure occurs:

Critical Stress:	σ_crit = S_r.crit·S_ty =
Critical Stress Intensity:	K_crit = K_r.crit·K_1C =

Reference Values

S_r.crit	=
K_r.crit	=

S_ty	=
K_1C	=

The Factor of Safety (FS) is based on length of the load line to the current point compared to the length of load line to the intersection (critical) point:

FS_FAD =

Residual Strength

The Factors of Safety (FS) for Residual Strength are given below. Full detailed calculations are provided in the following section.

FS on critical stress	FS_RSC.a
FS on critical crack length	FS_RSC.σ

Residual Strength Curve

The Residual Strength Curve shows the strength of the part as a function of crack size. If no crack is present, the part strength is equal to the yield strength. However, as the crack grows, the strength is reduced.

The Residual Strength Curve for the current case is shown below. The intersection of the current case with the curve in the vertical direction gives the critical stress for the current crack length. The intersection in the horizontal direction gives the critical crack length for the current applied stress level.

The critical values for the current case are:

Critical Stress:	σ_crit =
Critical Crack Length:	a_crit =

The Factors of Safety (FS) for the current case are:

FS on critical stress:

FS on critical crack length:

Reference Values

σ_cmb	=
a	=

σ_crit	=
a_crit	=

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Download Inputs File

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