Memoria Investigaciones en Ingeniería, núm. 26 (2024). pp. 98-124
https://doi.org/10.36561/ING.26.7
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
Este es un artículo de acceso abierto distribuido bajo los términos de una licencia de uso y distribución CC BY 4.0. Para ver una
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Memoria Investigaciones en Ingeniería, núm. 26 (2024). pp. 98-124
https://doi.org/10.36561/ING.26.7
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
Este es un artículo de acceso abierto distribuido bajo los términos de una licencia de uso y distribución CC BY 4.0.
Para ver una copia de esta licencia visite https://creativecommons.org/licenses/by/4.0/
Fatigue Life Estimation for Different Geometrical Configuration of Load-
Carrying Cruciform Joint using ABAQUS and Fe-Safe
Estimación del Tiempo de Fatiga para Diferentes Configuraciones Geométricas de
Juntas Cruciformes Portadoras de Carga utilizando ABAQUS y Fe-Safe
Estimativa do Tempo de Fadiga para Diferentes Configurações Geométricas de
Juntas Cruciformes Portantes usando ABAQUS e Fe-Safe
Zulqarnain Mukhtar Mahmood
1
, Muhammad Asif
2
(*), Syed Asad Ali Zaidi
3
Recibido: 03/02/2024 Aceptado: 29/03/2024
Summary. - This research paper focuses on the fatigue analysis of load-carrying cruciform joints made up of thick
plates, which are crucial components in ship structures. The study investigates the fatigue life of fillet welded cruciform
joints using both 2D and 3D geometries. Various loading conditions and boundary conditions are considered, and an
elastic-plastic finite element analysis is conducted using ABAQUS 2021. The number of cycles to failure is estimated
using Fe-Safe and the strain-based Brown Miller Morrow model. The results, presented through contour plots, Log
Life repeats, and Load Range vs. Number of Cycles graphs, reveal the fatigue behavior and failure locations.
Additionally, the methodology is validated against experimental data from literature, demonstrating its applicability.
The findings provide insights into the fatigue characteristics of load-carrying cruciform joints in thick plates,
contributing to enhanced design and reliability in the shipbuilding industry.
Keywords: Load-carrying Cruciform joint, Fatigue analysis, Elastic-Plastic FEA, ABAQUS, Fe-Safe, 2D and 3D
Cruciform geometries.
(*) Corresponding Author
1
Bachelor of Engineering, Department of Naval Architecture, Pakistan Navy Engineering College, National University of Sciences and
Technology (Pakistan), zulqarnainmukhtar622@gmail.com, ORCID iD: https://orcid.org/0009-0003-4412-0477
2
Assistant Professor, Department of Naval Architecture, Pakistan Navy Engineering College, National University of Sciences and Technology
(Pakistan), muhammadasif@pnec.nust.edu.pk, ORCID iD: https://orcid.org/0000-0003-4318-8253
3
Assistant Professor, Department of Mechnaical Engineering, Faculty of Engineering, Islamic University of Madinah (Saudi Arabia),
Sali@iu.edu.sa, ORCID iD: https://orcid.org/0000-0001-5457-5684
Z. M. Mahmood, M. Asif, S. A. Ali Zaidi
Memoria Investigaciones en Ingeniería, núm. 26 (2024). pp. 98-124
https://doi.org/10.36561/ING.26.7
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay 99
Resumen. - Este trabajo de investigación se centra en el análisis de fatiga de uniones cruciformes portadoras de
carga formadas por placas gruesas, que son componentes cruciales en las estructuras de los barcos. El estudio
investiga la vida a fatiga de uniones cruciformes soldadas en ángulo utilizando geometrías 2D y 3D. Se consideran
varias condiciones de carga y condiciones de contorno, y se realiza un análisis de elementos finitos elástico-plástico
utilizando ABAQUS 2021. El número de ciclos hasta la falla se estima utilizando Fe-Safe y el modelo Brown Miller
Morrow basado en deformaciones. Los resultados, presentados a través de gráficos de contorno, repeticiones de
registro de vida y gráficos de rango de carga versus número de ciclos, revelan el comportamiento de fatiga y las
ubicaciones de falla. Además, la metodología está validada con datos experimentales de la literatura, lo que demuestra
su aplicabilidad. Los hallazgos proporcionan información sobre las características de fatiga de las uniones
cruciformes que soportan carga en placas gruesas, lo que contribuye a mejorar el diseño y la confiabilidad en la
industria de la construcción naval.
Palabras clave: Unión cruciforme portadora de carga, Análisis de fatiga, FEA Elástico-Plástico, ABAQUS, Fe-Safe,
Geometrías cruciformes 2D y 3D.
Resumo. - Este trabalho de pesquisa concentra-se na análise de fadiga de juntas cruciformes de suporte de carga
compostas por placas espessas, que são componentes cruciais em estruturas de navios. O estudo investiga a vida à
fadiga de juntas cruciformes soldadas em ângulo usando geometrias 2D e 3D. Várias condições de carregamento e
condições de contorno são consideradas, e uma análise de elementos finitos elástico-plásticos é conduzida usando
ABAQUS 2021. O número de ciclos até a falha é estimado usando Fe-Safe e o modelo Brown Miller Morrow baseado
em deformação. Os resultados, apresentados através de gráficos de contorno, repetições de log de vida útil e gráficos
de faixa de carga versus número de ciclos, revelam o comportamento da fadiga e os locais de falha. Adicionalmente,
a metodologia é validada frente a dados experimentais da literatura, demonstrando sua aplicabilidade. As descobertas
fornecem informações sobre as características de fadiga das juntas cruciformes de suporte de carga em chapas
grossas, contribuindo para melhorar o design e a confiabilidade na indústria de construção naval.
Palavras-chave: Junta cruciforme portante, análise de fadiga, geometrias elástico-plásticas FEA, ABAQUS, Fe-Safe,
2D e 3D cruciformes.
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1. Introduction. - The construction of ships involves various types of connections, including stiffener joints and plate
joints, which are predominantly formed through welding processes. Cruciform joints are used to link longitudinal and
transverse structural parts of ships, such as the keel, its frames, and bulkheads. These joints are essential for transmitting
and distributing loads across the ship's hull, ensuring the vessel's structural integrity and strength. The load-carrying
ability of cruciform joint is critical for the ship to endure the numerous forces encountered during operation, such as
waves, the currents, and impacts loads. The proper design and construction of cruciform joints is critical to preventing
stress concentrations of fatigue, and structural failure.
The intersection of longitudinal and transverse elements of structure in a cruciform joint generates a complicated stress
field, with high stress concentrations located in the weld's toe and root. Geometric discontinuities, weld flaws, and
residual stresses induced during the fabrication procedure can all contribute to higher stress concentrations. Welding
plays a crucial role in the shipbuilding industry, but it also poses the risk of failures occurring in these joints during the
ship's commissioned life. Among the significant joints in ship structures are the cruciform welded joints or connections.
These joints experience high loads and are critical to the structural integrity of the ship. Therefore, it is essential to
conduct a comprehensive fatigue analysis to ensure their reliability and longevity.
Traditional fatigue evaluation techniques, such as nominal stress and hot-spot stress methods, frequently rely on
simpler stress estimations that may not adequately represent the intricate stress distributions found in cruciform joints.
Furthermore, empirical relationships based on limited data from experiments, like S-N curves or as notch factor
methods, may not sufficiently account for the distinctive geometric and material properties of a particular cruciform
joints design, potentially leading to discrepancies in fatigue life estimates.
Benefits of FEA include detailed stress analysis include a more in-depth and accurate assessment of the stress
distribution inside a cruciform joint, taking into account the intricate geometry, the properties of the material, loading
conditions, and weld-specific characteristics like the weld profile, residual stresses, as well as the presence of defects.
Engineers can also undertake parametric studies to optimize the joint's design and material properties, and the findings
can be tested versus experimental evidence, allowing for the improvement and validation of the models used for
analysis to assure better fatigue life forecasts.
The present research paper focuses on the fatigue analysis of fillet welded load-carrying cruciform joints made up of
thick plates. The study involves both 2D and 3D geometries, considering various boundary conditions. The analysis is
performed using elastic-plastic finite element analysis (FEA) conducted in ABAQUS 2021. The number of cycles to
failure is estimated using Fe-Safe and the strain-based Brown Miller Morrow model. To accurately model the behavior
of the joints, the material properties of SAE1045 steel are considered.
The findings of this research have significant implications for the shipbuilding industry. Understanding the fatigue
behavior of load-carrying cruciform joints in thick plates enables engineers and designers to make informed decisions
regarding their design, fabrication, and maintenance. By identifying critical areas prone to fatigue damage and
optimizing the joint configurations, the structural integrity and longevity of ships can be enhanced.
Moreover, the research contributes to the broader field of fatigue analysis and structural engineering. The methodology
employed in this study can be extended to other types of joints and structures, providing a framework for evaluating
fatigue life and enhancing the reliability of various engineering applications. The specific objectives include:
a) Investigating the fatigue behavior of cruciform joints under various loading conditions.
b) Assessing the influence of 2D and 3D geometry and different boundary conditions to investigate the fatigue
characteristics, failure locations, and stress distributions within the joints.
c) Estimating the number of cycles to failure using elastic-plastic FEA and the strain-based Brown Miller
Morrow model.
d) Validating the proposed methodology by comparing the simulated results with experimental data from the
literature.
The contribution of this research is three-fold. Firstly, to analyze the fatigue life of the cruciform joint through the 3D
geometry under varying load magnitudes ranging from 480 to 680 MPa. Secondly, to investigate the fatigue
performance of the joint through the 2D geometry under different boundary conditions, including axial loading, vertical
loading, bending, and combined axial-bending loading. Lastly, to validate the methodology employed in this study by
comparing the simulation results with experimental data from the literature.
The significance of this research lies in its contribution to the understanding of fatigue behavior in load-carrying
Z. M. Mahmood, M. Asif, S. A. Ali Zaidi
Memoria Investigaciones en Ingeniería, núm. 26 (2024). pp. 98-124
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cruciform joints of thick plates. The findings will aid in the development of more reliable and durable joint designs for
ship structures, thereby improving the overall structural integrity and safety of vessels. Furthermore, the research
methodology and insights gained can be extended to other applications that involve welded connections subjected to
cyclic loading conditions.
The organization of this paper is as follows: Section 2 provides a literature review on fatigue analysis of welded joints
and previous studies related to load-carrying cruciform joints. Section 3 describes the methodology employed,
including the finite element modeling techniques, material properties, and numerical simulations. Section 4 presents
the results and discussions, including contour plots, Log Life repeats, and Load Range vs. Number of Cycles graphs.
Section 5 focuses on the validation study by comparing the simulated results with experimental data from the literature.
Finally, Section 6 concludes the paper and discusses the implications of the research findings, along with suggestions
for future work.
Fatigue refers to the processes that occur when a material is subjected to cyclic stress, resulting in accumulated
degradation and, finally, final fracture. Waves produced in oceans are seen as cyclic excitations applied on a ship while
it is at sea. These loads have the potential to cause fatigue damage in structures of ships. The forces generated by the
ship's movement (such as rolling and pitching), wind movement, and green water motion are eventually transferred to
the ship hull through the lashing bridge structure [1]. Modern ship’s structure face serious fatigue damage concerns
due to increased ship's tonnage capacity and substantial usage of strong steel [2]. As histories and subsequent service
experiences have revealed, fatigue and fracture are key failure causes of ships [3]. The most typical problems in marine
vessel's structures during operational activities include fatigue fractures, panel's buckling, indents, and rusting. Fatigue
damages, in particularly, play a vital role in ship structures [4]. See Error! Reference source not found. for phases
of fatigue life.
Figure I. Fatigue Life Phases
The plate is a flat structural component having a thin thickness in comparison to its surface size and dimensions. When
working with plates, it is common to be perplexed by the subject of how to describe thin or thick plate, or which plate
is regarded thicker. According to [5] ratio of thickness to width or thickness to a length less than 10% is regarded as a
thin plate, while a ratio higher than 10% is called a thick plate. Thicknesses of thin plates range from 0.1 > t > 0.01
and thick plates have a thickness (t) higher than 0.01 [6].
Welding is a widely used manufacturing process in shipbuilding, and they are roughly divided into two types: (1)
Welding which relies only on heat source, such as fusion welding. (2) Welding which combines heat and pressure
sources, such as forge welding [7]. As welding is a fundamental connecting procedure in shipyards, this procedure
resulted in welding deformities, which caused numerous issues during the manufacturing of ships [8]. Welding errors
can occur because of a welder's inexperience, the use of wrong substances or faulty welding processes, and
environmental circumstances [9]. As a large quantity of corrected work is needed, welding imperfections lower the
fabrication quality of the ship's hull blocks and lead to poor productive performance [10].
The welded load-carrying cruciform joints (LCJs) are one of the most common connection types in shipbuilding or
maritime engineering projects, and fatigue failure to these is a serious hazard to welded constructions [11]. When
cruciform joints are exposed to continually changing stresses, they become fatigued [12]. Many types of research have
been performed related to fatigue assessment load-carrying cruciform joint (LCJ) and non-load carrying cruciform
joint (NLCJ) in literature. This joint is one of the important welded joints for ship structure during ship’s construction
[13].
Work done by [14] examined the quality of weld and fatigue of NLCJs made by VAG laser and MAG Hybrid welding
to produce four lots for testing and find stress concentration factors by applying finite element models with the help of
defined parameters of the local geometry of weld. Fatigue of LCJs contain incomplete weld penetration and under-
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matching strength of weld deposit and base metal were studied by [15] performing experiments of high and low cycle
fatigue on specimens. Research was performed by [16] to analyze fatigue strength affected by the size of cruciform
welded joints exposed axial as well as bending stresses. The research in [17] investigates the fatigue modeling or
simulation of high-performing steel joints formed by welding by utilizing notched stress and strain-based methods,
linear elastic fracture mechanics (LEFM), and SED (strain energy density).
For location of fatigue failure, a study by [18] consider notch stress intensity concept based on William’s explanation
in LEFM as well as ponder the weld size, transverse plate thickness, incomplete penetration, and plate thickness.
Three geometrically multifarious structural details of the ship were studied and analyzed [19] to estimate their fatigue
life using local approaches. All details have communal characteristics like Cruciform joints (two plates crossing each
other). A comparative study for fatigue behavior of high cycle fatigue, applied on steel LCJs made by welding was
performed by [20] at weld toe and root using PSM (peak stress method) and notch SIF (stress intensity factor).
Experimental and theoretical work has been done by [21] to study the effect of cooling and welded bead profile made
by shielded metal arc welding process for fatigue life of cruciform joint formed by 8 mm thick plates made up steel
ASTM A36 HR.
Some researchers [22] used relationship of RSG (relative stress gradient) and SCF to Notch factor ratio to study the
effect caused by the thickness of plates, the radius of weld toe, and bead profile for fatigue of cruciform welded joints.
A parametric study for the calculation of notch SCF using spline shape weld model during finite element analyses had
performed by [23] for cruciform welded joints experiencing unalike loading scenarios. The research of [24] propose
new formulas for SCFs for cruciform joints containing fillet welds subjected to bending loads after employing extended
numerical solutions of finite element methods. To study the penetration of weld (full and incomplete) for both fillet
welded LCJs and NLCJs had done by [25] with the help of 3D FEM. Strain energy density (SED) approach was used
by [26] to investigate parameters like scale effect, bead penetration, length of weld leg, and dimensions of plates for
cruciform joints.
Fatigue of fillet welded LCJs made up of austenitic stainless steel investigated by [27] using SN curve, fatigue crack
growth, and shape along with prediction method of fatigue life. An evaluation was proposed in [28] to find full fatigue
(crack initiation + crack propagation) of cruciform joint prepared by 7005 aluminum alloy considering residual stresses
produced after welding. The research work of [29] proposed new equations for SIF at the crack of weld toe for welded
LCJ with help of 3D finite element analysis to identify the failure site. To inspect LCF and HCF, a novel energy
analytical solution for weld toe and root of welded LCJs made up of 10CrNi3MoV steel was studied in [30] considering
the effects of weldment’s plasticity and mechanical heterogeneity based on Neuber’s Fictitious Notch Rounding
concept. The paper [31] re-analyzed the fillet welded LCJs for which failing occur at weld roots and compare results
of nominal and notch stress methods for fatigue strength. Some key findings of related research are listed in Table I.
Study
Fatigue Analysis
Approach
Key Findings
Wei Song et al. [20]
PSM and Notch SIF
A comparative study for fatigue behavior of HCF, applied
on steel welded LCJs at weld toe and root.
Oscar and Nelson [21]
Experimental and
Theoratical
Find fatigue life due to effect of cooling and welded bead
profile made by shielded metal arc welding process.
Toru and Naoki [22]
RSG, SCF and Notch
Factor
Study the effects caused by the thickness of plates, the
radius of weld toe, and bead profile for fatigue of LCJ
Yixun Wang et al. [23]
Finite Element Analysis
A parametric study for the calculation of notch SCF for
fatigue of cruciform joints.
Wang Sub Shin et al.
[25]
3D Finite Element Model
Fatigue on the penetration of full and incomplete welded
LCJs and NLCJs
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Pietro Foti et al. [26]
Strain energy density
Investigate parameters like scale effect, bead penetration,
weld leg length, and dimensions of plates for cruciform
joints.
Yang Peng et al. [27]
Fatigue life Prediction
Method
Fatigue of fillet welded LCJs investigated by using SN
curve, fatigue crack growth, and shape.
Jianxiao Ma et al. [28]
Residual Stress Approach
Find full fatigue (crack initiation + crack propagation) of
cruciform joint
Haisheng Zhao et al.
[29]
3D Finite Element
Analysis
Identify the fatigue failure site for welded LCJ.
Wei Song et al. [30]
Neuber’s Fictitious Notch
Rounding Concept
Inspect LCF and HCF for weld toe and root of welded
LCJs made up of 10CrNi3MoV.
Table I. Key Findings of Related Research
The proposed research aims to build upon the existing body of knowledge by conducting a fatigue analysis of load-
carrying cruciform joints in thick plates. By employing both 2D and 3D geometries, the study seeks to provide a
comprehensive understanding of the fatigue behavior, failure locations, and fatigue life of these joints under various
loading conditions. The research findings will contribute to the design and optimization of load-carrying cruciform
joints in ship structures, enhancing their fatigue resistance and structural integrity.
2. Methodology. - This section contains the details about what methodology has been used for the present study and
it has been applied. It will discuss the joint and software used for the research. It has the following details:
2.1 ABAQUS. - Abaqus, originally known as ABAQUS, was built in 1978 as a simulation software package for
studying complex problems utilizing FEA simulations as well as models and designs made with the help of a computer
called computer-aided engineering or CAE. This software suite is composed of five core program applications.
Complete ABAQUS Environment (cae) is an application that is employed to make models of physical bodies and
investigation of machine-driven parts and systems. It is mostly used for pre-processing designs and models for
simulation as well as viewing the results of finite element analysis.
Standard or Implicit, is a common purpose analyzer for finite element analysis using an implicit type of integration
strategy. It is a traditionally used tool.
Explicit, used for the distinctive purpose of analyzing finite element problems that investigates highly non - linear
problems with several complicated connections under transient loading using an explicit integration approach.
Computational Fluid Dynamics (CFD) is an application used for problems related to fluid dynamics that deliver
innovative CFD competencies considering significant pretreatment and post-processing provision.
Electromagnetic, a software tool that is used for computer-based electromagnetic problems that address sophisticated
electromagnetic theoretical problems.
ABAQUS is a popular and robust software suite for finite element analysis (FEA) that provides extensive modeling
capabilities. Cruciform joints, which frequently display intricate stress distributions and distortion patterns, are a good
fit for this analysis method because of its ability to handle non-linear materials, complicated geometries, and a wide
range of loading situations. Predicting the fatigue behavior of a joint requires the software to be able to capture the
impacts of weld profiles, residual stresses, and various other manufacturing-related parameters on the stress
distribution inside the joint. Figure II depicts the general solution procedure in ABAQUS.
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Figure II. ABAQUS General Solution Sequence
2.2 Fe-Safe. - Fe-safe is the industry's first market accessible fatigue analysis program that focuses on current multi-
axial strain-based failure methodologies. It is known for its correctness, efficiency, and simplicity of use when
analyzing metals, rubber, thermo-mechanical, creep-fatigue, and the welded joints. Fe-Safe is a robust, all-inclusive,
and user-friendly package of failure analysis software for models of finite elements. It is used in conjunction with
commercialized FEA software packages to determine:
Occurrence of fatigue cracks
Estimating the commencing of fatigue cracks
To find Working stress safety factors
The chance of survival and persistence at various working lives
Cracks propagation probability
Fe-Safe will spontaneously select the most suited analytical approach for engineers who may not be fatigue specialists
and will approximate material characteristics if test results are not provided. Figure III depicts a general fatigue
analysis scheme in Fe-Safe.
Figure III Fe-Safe Fatigue Analysis General Scheme
2.3 Geometry Used (3D and 2D). - For the investigation, two types of cruciform joint geometry were explored. [25]
Gives the dimensions for 3D geometry. Figure IV shows an example of this. This geometry includes a 6 mm convex-
shaped fillet weld. SolidWorks was used to create a whole (plates + welds) 3D solid model. Figure V depicts a
SolidWorks model.
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Figure IV. Cruciform Joint 3D Dimensions [25]
Figure V. 3D Model made by SolidWorks.
Dimensions for the 2D geometry of the joint are derived from [32]. Figure VI shows an example of this. This shape
includes an 8 mm flat fillet weld.
Figure VI. Cruciform Joint 2D Dimensions
This 2D geometry was created in ABAQUS using the part creation feature. 1/4th of geometry was made for axial and
vertical loading cases. The rest of the cases are studied on half of the geometry. Figures 7 and Figure 8 show ABAQUS
2D models.
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Figure VII. 1/4th of the geometry made by ABAQUS.
Figure VIII. Half of the Geometry made by ABAQUS.
2.4 Material for Cruciform Joint. - SAE 1045 is the material used in this study. It is mild carbon steel that
is widely utilized in a variety of industries. Axles, bolts, connecting rods, pins, studs, shafts, spindles, and
other similar uses are common. It is obvious that these parts are frequently subjected to repeated loading.
As a result, increasing the fatigue resistance of SAE 1045 appears to be necessary. SAE 1045's chemical
composition is obtained from [33] and is presented in Table II.
Constituents
Carbon
Silicon
Manganese
Phosphorus
Sulfur
Iron
Weight %
0.423
0.20
0.56
0.008
0.02
rest
Table II. SAE 1045 Chemical Composition
The monotonic characteristics are achieved [34] by utilizing a 25 KN servo-hydraulic machinery to perform
a uniaxial cycle test with a stress ratio of R = -1. During the test, a 2-mm strain gauge was affixed to the
specimen to gather strain events. See Figure 3.8 for servo-hydraulic machinery and Table III for SAE 1045
monotonic properties.
Properties
Values
Ultimate Tensile Stress () (UTS)
798 MPa
Yield Stress ()
414 MPa
Young’s Modulus (E)
198 MPa
Table III. SAE 1045 Monotonic Properties
Following that, a cycle test [34] was performed at various percentages of UTS (ultimate tensile strength)
acquired from the preceding tensile test. The percentages used are 60, 65, 70, 80, and 85 percent. As a result,
five various stress values were used to capture failure time and strain range readings. See Table 3.3 for more
information.
Applied Stress (MPa)
Strain Ranges ()
480 (60 % of UTS)
2294
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520 (65 % of UTS)
3200
570 (70 % of UTS)
4059
640 (80 % of UTS)
4565
680 (85 % of UTS)
5800
Table IV. Applied Stresses for Cyclic Test and Strain Ranges
2.5 Elastic-Plastic FEA. - ABAQUS is used for elastic-plastic finite element analysis. First, a 3D model made by
SolidWorks is loaded into ABAQUS, and the 2D geometry of a cruciform joint is created in ABAQUS using the Sketch
and Feature tools. Static General STEP is built for plastic analysis after specifying the elastic and plastic material
characteristics of SAE 1045. As previously stated, two configurations are being investigated. As a result, for 3D
geometry, one type of boundary condition along with axial loadings of 480, 520, 570, 640, and 680 MPa are
investigated. One side is fixed, upper and lower face of cruciform joint is allowed to move and the side opposite to
fixed side is subjected to axial loading. For more information, see Figure X. In the current study, 2D geometry is
subjected axial loading for same loading values as of 3D geometry and boundary conditions. For Meshing, an 8-node
biquadratic plain strain element CPE8R with reduced integration is utilized. After the work is completed, the findings
are taken in the form of stress and deformation contours. The whole flow diagram of elastic-plastic FEA may be found
in Figure IX.
Figure IX. Elastic-Plastic FEA Flowchart
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Figure X. Loading Scenario and Boundary Condition for 3D Geometry
2.6 Strain Based Brown Miller Morrow. - According to the Brown-Miller model, much fatigue impairment happens
on that plane or surface which is under the influence of the maximum amplitude value of shear strain, and the
impairment or failure is an accumulation of both; the shear strain and the strain perpendicular to that plane [35]. See
Figure XI.
Figure XI. Normal and Shear Strain Description [35]
The Brown-Miller model offers the most accurate life predictions for ductile metals but is less accurate for brittle
metals. It is a critical plane-based multi-axial fatigue processing algorithm that employs surfaces or planes at a right
angle to the surface as well as planes at 45º to the surface. This model focuses on the plane within the material where
the likelihood of crack initiation is the highest. It has following key limitations:
It does not consider non-proportional loadings for fatigue life.
It lacks to consider mean stress effects on fatigue life.
It does not explicitly consider progressively accumulation of damage during fatigue.
For materials, it is assumed that the materials are ductile that exhibits plastic deformation before failure. Material is
homogenous and isotropic which means that their properties are uniform and does not change direction of loading.
An elastic FEA's stress results are required for this algorithm. To estimate elastic-plastic analysis-based stress strains
outcomes from the source of elastic FEA stresses, multi-axial type elastic-plastic based corrections are employed [36].
If
Then from the strain circle of Mohr
And
In case of uniaxial plain stress
And
Then
And
But, the conservative strain life prediction equation is
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It can be re-written by considering the amplitudes of shear and normal strains on the left-hand side as
Elastic Plastic
For elastic stress cases, the Poisson ratio is
Then
Also
Then the constant will be
And similarly, for a plastic case, the Poisson ratio is
Then
And
So, the constant will be
Hence, the complete Brown Miller equation for strain life will become
The researchers Kandil, Brown, and Miller created this version of the Brown-Miller parameter.
The strain-life equation is changed for mean stress correction proposed by Morrow:
This approach may also be used to analyze the fatigue of elastic-plastic FEA data [36].
2.7 Fatigue Analysis Using Fe-Safe. - Fe-safe is the industry's first commercially accessible fatigue analysis program
that focuses on current multiaxial strain-based fatigue methodologies.
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Figure XII. Combined ABAQUS and Fe-Safe Flowchart for Fatigue Analysis
Figure XIII. Fe-Safe Fatigue Life Prediction Flow Chart
The schematic illustration of fatigue analysis utilizing ABAQUS and Fe-Safe is shown in Figure XII. It is known for
its accuracy, speed, and ease of use when analyzing metals, rubber, thermo-mechanical and creep fatigue, and welded
joints. Fe-Safe is a robust, all-inclusive, and user-friendly packages of fatigue analysis tools for finite element models
[37]. The flowchart for Fe-Safe working is shown in Figure XIII. The worst life repeats represent the number of cycles
to failure for estimation of fatigue life of joint.
3. Results & Discussion. - This chapter includes the results and discussions of outcomes obtained from the above-
mentioned methodologies. Results are shown in the form of contours, tables, graphs, or curves. First, the 3D geometry
of Load-carrying Cruciform Joint (LCJ) is discussed and then after that, the loading scenarios and boundary conditions
for 2D are detailed.
3.1 Results of 3D Geometry. - As mentioned in the previous chapter that this geometry has been studied for five
different loadings and only one type of boundary condition. This was done to understand the fatigue analysis process
using ABAQUS and Fe-Safe to perform a detailed study on different loading and boundary conditions for 2D geometry.
In this context, five loadings are applied on 3D geometry ranging from 480 to 680, and the contour shown in Figure
XIV is for the last loading value i.e., 680 MPa. Figure XV shows the results of fatigue life obtained by Fe-Safe.
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Figure 1: Contour of 3D Geometry for 680 MPa from ABAQUS
Figure 2: Fatigue Life for 3D Geometry obtained from Fe-Safe
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3.2 Discussion. - Linear hexahedral elements of type C3D8R are used for the Meshing of 3D geometry. The total
number of elements and nodes are 12640 and 17613. The boundary conditions are applied in such a way that the plate
end opposite to the applied load is fixed while the other top and bottom ends are allowed to move in the direction of
applied stress regarding Figure 10. From Figure 14, the most crucial region exists on the main plate where the value
of Von Mises stress is 680 MPa. It is on element 7311 having node 965. So, one can say that a joint failure will occur
on that element. But it is not on the same element as shown by Figure 15. According to this, element 5211 with node
20 has minimum Log Life which means that failure occurs on that element, not on element 7311. This element lies in
the fixed end region as is clear in Figure 15. Log Life repeats are used for representing the number of cycles to failure.
The minimum value of Log Life shows that such element or region will fail earlier than other elements or regions of a
structure. Hence, as a result, structure damage occurs after a certain number of repetitions of the applied load. Table 5
contains outcomes for each applied load.
Figure XVI. SN-Curve for 3D Geometry of Joint
Results for 3D Geometry
Applied Stress (MPa)
No. of Repeats
480
16773.326
520
10354.495
570
5281.393
640
3448.218
680
3318.614
Table V. Number of Repeats for each Applied Load on 3D Geometry
Using values of Table V, a graph is made to represent SN-Curve for 3D geometry of Cruciform joint. See Figure
XVI.
3.3 Results of 2D Geometry. - For 2D geometry, the axial load applied ranges from 100 to 500 MPa with an equal
difference of 100 MPa. But, for each case, only the outcomes obtained after applying maximum load i.e. 500 MPa are
shown in the following figures. It is chosen because, at maximum value, it is better to study the structural changes
occurred in the joint to show extreme behavior at higher loading condition. See Figure XVII for results obtained from
elastic-plastic FEA in ABAQUS and Figure XVIII for the number of cycles got from Fe-Safe.
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Figure XVII. Contour of Axial Load of 500 MPa from ABAQUS
3.4 Discussion. - Quadratic quadrilateral elements of type CPE8R are used for the Meshing of 2D geometry. The total
number of elements and nodes are 547 and 2036. The boundary condition type 1 is such that in which 1/4th of 2D
geometry is considered due to symmetry for elastic-plastic FEA and in which attached plate end opposite to applied
stress is allowed to move in the vertical direction and the lower end of main plate is allowed to move in the horizontal
direction. From Figure XVII, the most critical area exists on fillet weld toe where the value of Von Mises stress is
556.2 MPa. It is on element 485 having node 10. So, it is obvious to say that joint damage will occur to that element.
And it is the same element as shown in Figure XVIII. According to this, element 485 with node 10 has minimum Log
Life repeats which means that failure occurs on that element. This element lies in the weld toe region as is clear in
Figure XVIII. Log Life repeats are used for signifying the number of cycles to failure. Table VI contains the results
for each applied axial load.
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Figure XVIII. Fatigue Life for Axial Load of 500 MPa obtained from Fe-Safe
Results for Axial loading
Applied Stress (MPa)
No. of Repeats
480
432123.5
520
347315.469
570
21706.598
640
6183.626
680
6141.355
Table VI. Number of Repeats for Axial Load on 2D Geometry
Using values of Table VI, SN-Curve for axial loading is made. See Figure XIX.
Figure XIX. SN-Curve for Axial loading applied 2D Geometry.
3.5 Comparison of Results (3D & 2D Geometry). - Comparison of results for 3D and 2D geometry is shown in
Figure XX for better understanding of the trends of SN-curves. At load 480 MPa, there is large difference between
number of cycles of both geometry and when becomes closer to 600 MPa, the curves for both begin coinciding with
each other. It means both geometries show the same fatigue behavior at higher loadings when consider strain-based
Brown Miller Model for fatigue estimation.
Figure 3: Comparison of Results
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4. Validation Study. - For validation study of methodology, the data are taken from [38]. The data is composed of
eight different geometrical configurations of welded Cruciform joints. Each joint has four welds with different
horizontal and vertical dimensions. See Figure XXI for a 3D geometry description.
Dimensions of each weld detail for eight samples are given Table VII. The sample numbers used in that table are the
same as in Table II of [11]. The width of the main plate is denoted by “L” and the thickness of the attached plates is
indicated by “t”. All the dimensions are in millimeters (mm).
Figure XXI. Description of symbols used for geometry.
Sample
No.
Weld 1 (mm)
Weld 2 (mm)
Weld 3
(mm)
Weld 4 (mm)
L
t
h1
v1
h2
v2
h3
v3
h4
v4
(mm)
(mm)
19
8.13
8.52
7.25
8.6
8.5
8.62
7.8
9.63
35
12
6
10.27
10.36
9.82
11.56
9.9
11.9
8.85
10.21
35
12
5
10.57
10.52
10.11
12.94
10.08
12.08
9.05
9.87
35
12
4
10.19
10.21
10.56
11.89
10.49
11.38
8.82
9.9
35
12
18
8.89
12.33
6.91
10.94
10.49
11.1
10.8
11.93
35
12
3
10.27
10.36
9.82
11.56
9.9
11.9
8.85
10.21
35
12
2
10.57
10.52
10.11
12.94
10.08
12.08
9.05
9.87
35
12
1
10.19
10.21
10.56
11.89
10.49
11.38
8.82
9.9
35
12
Table VII. Details of Eight Samples used for the validation study
4.1 Experimental Data. - Experimental data contain the number of fatigue cycles, location of the fracture, and applied
loads concerning each sample mentioned in Table VII. Experimental data are given in Table VIII.
Sample Number
Cases
Applied Load (MPa)
Fatigue Cycles
Fracture Location
19
C1
100
320500
Weld Root
6
C2
200
224700
Weld Toe
5
C3
240
129600
Weld Toe
4
C4
280
56580
Weld Toe
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18
C5
305
53500
Weld Toe
3
C6
320
46800
Weld Toe
2
C7
360
37800
Weld Toe
1
C8
400
21500
Weld Toe
Table VIII. Experimental data detail
A 250‐KN electro-hydraulic servo testing machine MTS 809 coupled with a load‐control condition was used to conduct
higher cycle fatigue experimentations of load-carrying Cruciform joint.
4.2 Material for Joint. - The SAE 1045 is the material used in this study. It is mild carbon steel that is widely utilized
in a variety of industries. Axles, bolts, connecting rods, pins, studs, shafts, spindles, and other similar uses are common.
It is obvious that these parts are frequently subjected to repeated loading. As a result, increasing the fatigue resistance
of SAE 1045 appears to be necessary. SAE 1045's chemical composition is obtained from [33] and is presented in
Table IX.
Constituents
Carbon
Silicon
Manganese
Phosphorus
Sulfur
Iron
Weight %
0.423
0.20
0.56
0.008
0.02
rest
Table IX. SAE 1045 Chemical Composition
The monotonic characteristics are achieved [34] by utilizing a 25 KN servo-hydraulic machinery to perform a uniaxial
cycle test with a stress ratio of R = -1. During the test, a 2-mm strain gauge was affixed to the specimen to gather strain
events. See Table X for SAE 1045 monotonic properties.
Properties
Values
Ultimate Tensile Stress ()
798 MPa
Yield Stress ()
414 MPa
Young’s Modulus (E)
198 MPa
Table X. SAE 1045 Monotonic Properties
Following that, a cycle test [34] was performed at various percentages of UTS (ultimate tensile strength) acquired from
the preceding tensile test. The percentages used are 60, 65, 70, 80, and 85 percent. As a result, five various stress values
were used to capture failure time and strain range readings. See Table XI for more information.
Applied Stress (MPa)
Strain Ranges ()
480 (60 % of UTS)
2294
520 (65 % of UTS)
3200
570 (70 % of UTS)
4059
640 (80 % of UTS)
4565
680 (85 % of UTS)
5800
Table XI. Applied Stresses for Cyclic Test and Strain Ranges
4.3 Conducting Elastic-Plastic FEA. - ABAQUS is used for elastic-plastic finite element analysis. First, the 3D
geometry of a cruciform joint is created in ABAQUS using the Sketch and Feature tools. Static General STEP is built
for plastic analysis after specifying the elastic and plastic material characteristics of SAE 1045. In the current case,
eight distinct types of geometrical configurations are investigated for fatigue cycles, for loading values of 100, 200,
240, 280, 305, 320, 360, and 400 for the same boundary condition. For Meshing, an 8-node linear hexahedral element
of type C3D8R with reduced integration is utilized. The whole flow diagram of boundary and loading conditions can
be seen in Figure XXII. The right and left ends are allowed to move in x, y and z direction while all rotations are
forbidden. On the upper and lower end of the joint load is applied. The loading nature is cyclic tensile, and zero weld
penetration is considered because of the technique of wire electrode cutting [11]. All eight configurations were made
separately keeping the other dimensions constant.
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Figure XXII. Loading and boundary conditions on cruciform joint.
4.4 Fatigue Analysis Using Fe-Safe. - Fe-safe is the industry's first commercially accessible fatigue analysis program
that focuses on current multiaxial strain-based fatigue methodologies. The schematic illustration of fatigue analysis
utilizing ABAQUS and Fe-Safe is shown in Figure XXIII. It is known for its accuracy, speed, and ease of use when
analyzing metals, rubber, thermo-mechanical and creep fatigue, and welded joints. Fe-Safe is a robust, all-inclusive,
and user-friendly packages of fatigue analysis tools for finite element models [37]. The worst life repeats represent the
number of cycles to failure for estimation of fatigue life of joint.
Figure XXIII. Fatigue analysis using ABAQUS and Fe-Safe
4.5 Simulation Results. - The simulated results are shown in the form of Log Life repeats contours. Figure XXIV
contains contours of each eight configurations for their respective loadings i.e., 100, 200, 240, 280, 305, 320, 360, 400
MPa. Each contour indicated the region in which minimum Log Life repeats occur with a highlighted area. For all
cases, the fatigue damage location is not the same because of the irregular or nonlinear plastic nature of the material.
After that, Table XII is made to show the differences between the simulated and experimental number of cycles,
percentage errors, and the failure locations for eight samples. Finally, Figure XXV shows a graph representing both
simulated and experimental curves.
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Sample
Number
Applied
Load (MPa)
Simulated
Cycles
Experimental
Cycles
%
Error
Fracture Location
19
100
324776
320500
1.316
Weld 3 Toe on the
lower plate
6
200
234804
224700
4.303
A little bit below of
Weld 4 Toe on the
lower plate
5
240
135127
129600
4.090
Weld 4 Toe on the
lower plate
4
280
57215
56580
1.109
On upper Plate above
Weld 2
18
305
56794
53500
5.799
Lower Plate below
weld 3
3
320
50186
46800
6.746
The backside of the
upper plate above weld
1
2
360
38610
37800
2.097
The backside of the
upper plate above weld
1
1
400
21648
21500
0.683
Near to back end on
the upper plate
Table XII. Detail of Simulations for Eight samples.
Figure XXV. Simulated and Experimental SN-Curve
5. Conclusions. - The conclusions for 3D geometry, 2D geometry and validation study are as follows:
5.1 3D Geometry. –
The fatigue failure occurs on that element that did not lie on the lower surface of the main plate. Rather, it
lied on the fixed end of the main plate.
Although the whole plate is under extreme loading as shown in Figure XIV, the accumulated effect of applied
load cause failure only on the element of the fixed end side.
As stated, earlier results of only the higher loadings were displayed, so, it may be possible that in other cases
the element of failure would not be the same.
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The SN-Curve for 3D geometry shows large differences in the number of repeats for small loading values i.e.,
from 480 to 640 MPa.
When the load of 680 MPa was applied, the fatigue damage occurred rapidly after a few repeats showing a
very small difference as compared to previous values.
The abrupt fatigue failure due to large load is also making the sense of corresponding to larger load
applications.
5.2 2D Geometry. –
The applied load causes tension in the weld joint; opposite to the case of 3D geometry, in which applied load
cause compression.
The most affected zone due to tension is at the weld toe. The same region is also highlighted by Fe-Safe
results.
The SN-Curve for this case showed huge differences between the number of repeats when the applied loads
were small.
The difference became small as the load exceeded 500 MPa indicating the occurrence of fatigue damage after
a few thousand repeats as compared to small loads.
This is true because higher loads cause faster plastic deformation accompanied by large strains.
5.3 Validation Study. - Following are the key findings with reference to Table XII and Figure XXV:
The simulated results show that the fracture locations are different for most of the samples from the region
obtained by experimental results.
The number of cycles attained after the simulation is greater than the experimental for each sample.
Most of the fracture locations are identified near the weld toes region except for toes of weld 3 and weld 4.
No weld root failure has been identified for any weld and no failure occurs for toes of weld 1 and weld 2.
The lower plate is in a severe situation because weld 3 and weld 4 are located on lower plate, joining the main
plate.
Since no fracture occurred on weld 1 and weld 2, the most crucial region for upper plate is the backside of the
plate.
No fracture occurred on the main plate and toes of welds situated on the main plate because loading is tensile
causing fracture on weld toes situated on upper & lower plates and on the lower & upper plates separately.
The graph in Figure 25 shows that at higher loads, fatigue failure occurs after few thousand repeats due to
abrupt plasticity behavior in material and for lower loads, it takes more than 3 lacs repeats.
The lowest % error is 0.683 for Sample 1 with 400 MPa load and maximum % error is 6.746 for Sample 3
with 320 MPa load after simulation.
As the % error is less than 10 % for all cases, it shows that the simulated results by ABAQUS and Fe-Safe
are in acceptable range.
6. Recommendations. - Recommendations for improving designs of load carrying cruciform joints (LCJs) and for
future research directions are as follows:
6.1 Improving Design of Load Carrying Cruciform Joints. -
Increasing the radius of the weld toe helps minimize stress concentration, which is a typical site for fracture
development.
Adjusting weld leg length helps equally distribute loads throughout the joint and reduce localized stress
concentrations.
Weld reinforcement, like thicker welds or fillet connections, can improve joint strength.
High-quality welding techniques, including joint preparation, weld parameters that are and post-weld
examination, can reduce weld faults that cause stress.
Applying post-weld procedures, such as peening or thermal treatment, can lower residual stresses in the
connecting surfaces and prevent early fatigue cracks.
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6.2 Future Research Directions. -
Consider using modern materials like high-strength steels, aluminum alloys, as well as fiber-reinforced
composites to manufacture cruciform joints.
Investigate how material parameters, which include the tensile strength, yield strength, and resistance to
fatigue, affect joint load-carrying capability and fatigue life.
Incorporate more complicated loading situations, such as coupled axial, bending, as well as torsional loads,
that ship constructions often face.
Use sophisticated fatigue analysis approaches, such as critical plane techniques or energy-based theories, to
properly simulate joint performance for multi-axial fatigue loading.
Investigate how environmental factors such corrosive sea environments, temperature changes, and weathering
impact the functionality and endurance of cruciform joints.
Understand how additive manufacturing (AM) methods, such 3D printing, may be used to create cruciform
joints with customizable attributes and increased geometric complexity.
Investigate how AM-specific factors, including roughness of the surface and residual stresses, affect joint's
mechanical efficiency and fatigue life.
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Z. M. Mahmood, M. Asif, S. A. Ali Zaidi
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Z. M. Mahmood, M. Asif, S. A. Ali Zaidi
Memoria Investigaciones en Ingeniería, núm. 26 (2024). pp. 98-124
https://doi.org/10.36561/ING.26.7
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay 124
Nota contribución de los autores:
1. Concepción y diseño del estudio
2. Adquisición de datos
3. Análisis de datos
4. Discusión de los resultados
5. Redacción del manuscrito
6. Aprobación de la versión final del manuscrito
ZMM ha contribuido en: 1, 2, 3, 4, 5 y 6.
MA ha contribuido en: 1, 2, 3, 4, 5 y 6.
SAAZ ha contribuido en: 1, 2, 3, 4, 5 y 6.
Nota de aceptación: Este artículo fue aprobado por los editores de la revista Dr. Rafael Sotelo y Mag. Ing. Fernando
A. Hernández Gobertti.
