The document summarizes research on the delamination of a thin elastic film from a ductile substrate during indentation loading and unloading. A spherical rigid indenter is used. The interface is modeled as a cohesive surface that allows for small displacements. Tractions at the interface are modeled using uncoupled normal and tangential traction-separation laws. Results show the distribution of stresses and displacements in the film and substrate during loading and delamination upon unloading.
1) The document proposes using parallel computation to improve estimates obtained via the Independent Metropolis-Hastings (IMH) algorithm.
2) The block IMH algorithm runs multiple IMH chains in parallel on blocks of proposals, calculating acceptance ratios only once per block.
3) Experimental results on examples show the block IMH approach reduces variance compared to standard IMH, with different block ordering strategies explored.
The document describes polar coordinates and how to convert between polar and rectangular coordinates. Polar coordinates represent a point (P) using its distance (r) from a fixed point called the pole and its angle (θ) from a fixed line called the polar axis. The coordinate of P is written as P(r, θ). Relations show that to convert between polar (r, θ) and rectangular (x, y) coordinates, x = r cosθ, y = r sinθ, and r2 = x2 + y2. Common polar graphs are circles with r = k, ellipses with r = a sinθ or r = a cosθ, cardioids with r = a(1 + sinθ), and roses
This fourth installment of the 2012 KGWI
looks at issues surrounding job mobility and career progression as part of a shift to a more autonomous and empowered workforce. It shows a changing attitude on the part of employees, with more embracing the notion of gaining new experiences and skills with multiple employers.
The document summarizes research on modeling fatigue damage in solder joints. It describes modeling a solder bump with cohesive zones at material boundaries. Cyclic loading is applied and damage starts at interfaces with stiff particles, propagating throughout the bump over cycles. The model tracks damage distribution and total damage increase over cycles. As damage accumulates, the bump's stiffness and reaction force decrease. The cohesive zone approach shows promise for modeling fatigue damage evolution in solder joints.
1) A finite element method was used to simulate the indentation of a ductile substrate coated with a thin elastic film using a rigid spherical indenter.
2) During loading, delamination was found to initiate tangentially at a distance of two to three times the contact radius.
3) During unloading, a circular part of the coating directly under the contact area was lifted off from the substrate, indicating normal delamination. Normal delamination was seen as a hump on the load-displacement curve.
4) There was a critical interfacial strength above which delamination could be prevented for a given indentation depth and material system. The effects of residual stress in the film and interface waviness
1) The document proposes using parallel computation to improve estimates obtained via the Independent Metropolis-Hastings (IMH) algorithm.
2) The block IMH algorithm runs multiple IMH chains in parallel on blocks of proposals, calculating acceptance ratios only once per block.
3) Experimental results on examples show the block IMH approach reduces variance compared to standard IMH, with different block ordering strategies explored.
The document describes polar coordinates and how to convert between polar and rectangular coordinates. Polar coordinates represent a point (P) using its distance (r) from a fixed point called the pole and its angle (θ) from a fixed line called the polar axis. The coordinate of P is written as P(r, θ). Relations show that to convert between polar (r, θ) and rectangular (x, y) coordinates, x = r cosθ, y = r sinθ, and r2 = x2 + y2. Common polar graphs are circles with r = k, ellipses with r = a sinθ or r = a cosθ, cardioids with r = a(1 + sinθ), and roses
This fourth installment of the 2012 KGWI
looks at issues surrounding job mobility and career progression as part of a shift to a more autonomous and empowered workforce. It shows a changing attitude on the part of employees, with more embracing the notion of gaining new experiences and skills with multiple employers.
The document summarizes research on modeling fatigue damage in solder joints. It describes modeling a solder bump with cohesive zones at material boundaries. Cyclic loading is applied and damage starts at interfaces with stiff particles, propagating throughout the bump over cycles. The model tracks damage distribution and total damage increase over cycles. As damage accumulates, the bump's stiffness and reaction force decrease. The cohesive zone approach shows promise for modeling fatigue damage evolution in solder joints.
1) A finite element method was used to simulate the indentation of a ductile substrate coated with a thin elastic film using a rigid spherical indenter.
2) During loading, delamination was found to initiate tangentially at a distance of two to three times the contact radius.
3) During unloading, a circular part of the coating directly under the contact area was lifted off from the substrate, indicating normal delamination. Normal delamination was seen as a hump on the load-displacement curve.
4) There was a critical interfacial strength above which delamination could be prevented for a given indentation depth and material system. The effects of residual stress in the film and interface waviness
The document summarizes guidelines from the International Commission on Non-Ionizing Radiation Protection (ICNIRP) for limiting exposure to time-varying electric, magnetic, and electromagnetic fields up to 300 GHz. It establishes basic restrictions on exposure levels based on established health effects. It also provides reference levels to help determine if the basic restrictions are exceeded. The guidelines are intended to protect against known adverse health effects from exposure and will be periodically revised as more effects are identified.
This chapter examines analytical and empirical relations used to extract mechanical properties from indentation experiments. Finite element simulations are performed for spherical and conical indentation of elastic, elastic-plastic, and coated materials. The material response is characterized by load-displacement curves. Existing relations for contact area, contact stiffness, and hardness are compared to finite element results. The chapter lays groundwork for using indentation to characterize properties and failure modes of coated materials.
1) Indentation-induced failure of hard coatings is modeled using cohesive surfaces to represent interfacial delamination and coating cracking under normal and shear loads.
2) Results show that shear delamination occurs within the film along a shear plane, while normal delamination separates the film from the substrate.
3) Coating cracking is also observed radially around the indentation with high tensile stresses concentrated at the coating/substrate interface.
The document summarizes a study on modeling fatigue damage in solder interconnects using a cohesive zone approach. Key points:
1) A cohesive zone method is used to model fatigue damage accumulation in solder joints, representing the interface between continuum elements.
2) A damage evolution law based on experimental observations is used to model how damage increases with the number of loading cycles and applied load.
3) Results show the predicted damage distribution in a sample solder joint under cyclic loading, as well as the effects of mean strain and load sequencing on damage accumulation.
This document discusses simulating fatigue damage in solder joints using cohesive zone modeling. It introduces cohesive zone modeling as a numerical method to describe interface mechanics and model crack initiation and propagation. The document proposes using a cohesive zone model with a damage variable to simulate fatigue damage accumulation over successive loading cycles at solder interfaces. The model represents interfaces with cohesive elements having traction-separation laws that degrade nonlinearly based on a damage evolution law to capture fatigue failure below static strength limits.
This study measured environmental radioactivity in Palestine using in situ gamma-ray spectroscopy. Measurements were taken at 18 locations across the West Bank. The detected radionuclides were naturally occurring gamma emitters from 238U, 232Th and 40K decay chains, with 137Cs also identified at a few locations. Activity concentrations ranged from 8-203 Bq/kg for 40K, 6-32 Bq/kg for 238U and 5-30 Bq/kg for 232Th. The total outdoor gamma dose rate was calculated to be 6-30 nGy/h, with an average of 18 ± 7 nGy/h or about 30% of the world average. The results provide a baseline for environmental
This document summarizes a study that models fatigue damage in solder interconnects using a cohesive zone approach. The study simulates fatigue damage over successive loading cycles using finite element analysis. Damage is modeled to occur at interfaces using cohesive zones, which incorporate a damage variable into the constitutive law to account for material degradation over cycles. A damage evolution law is formulated to capture key damage characteristics as damage accumulates. The model predicts solder bump lifetime and shows good agreement with an empirical lifetime model. Damage distribution and stiffness loss are examined over cycles. The analysis is currently limited to 2D but aims to provide a more realistic fatigue simulation than models that assume constant material properties.
This document summarizes a numerical study of indentation-induced cracking in brittle coatings on ductile substrates. Finite element modeling was used to simulate indentation with a spherical indenter. The coating was modeled as linear elastic, the substrate as elastic-perfectly plastic, and cracks in the coating were modeled using cohesive surfaces. Circumferential cracks were found to initiate at the coating surface near the contact edge due to high tensile radial stresses. The first crack caused a kink in the load-displacement curve. The spacing between cracks was on the order of the coating thickness. The effects of material properties and cohesive parameters on crack initiation and spacing were also investigated.
This document summarizes a numerical simulation of indentation-induced delamination of an elastic film on an elastic-plastic substrate. The simulation models the interface between the film and substrate using a cohesive surface that allows for both normal and tangential displacement. It is found that delamination occurs in a tangential mode rather than a normal mode and is initiated at a distance of two to three times the contact radius. The speed of delamination propagation depends on the interfacial strength, with stronger interfaces producing higher initial speeds and lower steady state speeds. Indentation load vs. depth curves may exhibit a "kink" when delamination is initiated for interfaces of relatively high strength.
Unveiling Paul Haggis Shaping Cinema Through Diversity. .pdfkenid14983
Paul Haggis is undoubtedly a visionary filmmaker whose work has not only shaped cinema but has also pushed boundaries when it comes to diversity and representation within the industry. From his thought-provoking scripts to his engaging directorial style, Haggis has become a prominent figure in the world of film.
The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...greendigital
Leonardo DiCaprio, a name synonymous with Hollywood stardom and acting excellence. has captivated audiences for decades with his talent and charisma. But, the Leonardo DiCaprio haircut is one aspect of his public persona that has garnered attention. From his early days as a teenage heartthrob to his current status as a seasoned actor and environmental activist. DiCaprio's hairstyles have evolved. reflecting both his personal growth and the changing trends in fashion. This article delves into the many phases of the Leonardo DiCaprio haircut. exploring its significance and impact on pop culture.
Christian Louboutin: Innovating with Red Solesget joys
Christian Louboutin is celebrated for his innovative approach to footwear design, marked by his trademark red soles. This in-depth look at his life and career explores the origins of his creativity, the milestones in his journey, and the impact of his work on the fashion industry. Learn how Louboutin's bold vision and dedication to excellence have made his brand synonymous with luxury and style.
Everything You Need to Know About IPTV Ireland.pdfXtreame HDTV
The way we consume television has evolved dramatically over the past decade. Internet Protocol Television (IPTV) has emerged as a popular alternative to traditional cable and satellite TV, offering a wide range of channels and on-demand content via the internet. In Ireland, IPTV is rapidly gaining traction, with Xtreame HDTV being one of the prominent providers in the market. This comprehensive guide will delve into everything you need to know about IPTV Ireland, focusing on Xtreame HDTV, its features, benefits, and how it is revolutionizing TV viewing for Irish audiences.
Orpah Winfrey Dwayne Johnson: Titans of Influence and Inspirationgreendigital
Introduction
In the realm of entertainment, few names resonate as Orpah Winfrey Dwayne Johnson. Both figures have carved unique paths in the industry. achieving unparalleled success and becoming iconic symbols of perseverance, resilience, and inspiration. This article delves into the lives, careers. and enduring legacies of Orpah Winfrey Dwayne Johnson. exploring how their journeys intersect and what we can learn from their remarkable stories.
Follow us on: Pinterest
Early Life and Backgrounds
Orpah Winfrey: From Humble Beginnings to Media Mogul
Orpah Winfrey, often known as Oprah due to a misspelling on her birth certificate. was born on January 29, 1954, in Kosciusko, Mississippi. Raised in poverty by her grandmother, Winfrey's early life was marked by hardship and adversity. Despite these challenges. she demonstrated a keen intellect and an early talent for public speaking.
Winfrey's journey to success began with a scholarship to Tennessee State University. where she studied communication. Her first job in media was as a co-anchor for the local evening news in Nashville. This role paved the way for her eventual transition to talk show hosting. where she found her true calling.
Dwayne Johnson: From Wrestling Royalty to Hollywood Superstar
Dwayne Johnson, also known by his ring name "The Rock," was born on May 2, 1972, in Hayward, California. He comes from a family of professional wrestlers, with both his father, Rocky Johnson. and his grandfather, Peter Maivia, being notable figures in the wrestling world. Johnson's early life was spent moving between New Zealand and the United States. experiencing a variety of cultural influences.
Before entering the world of professional wrestling. Johnson had aspirations of becoming a professional football player. He played college football at the University of Miami. where he was part of a national championship team. But, injuries curtailed his football career, leading him to follow in his family's footsteps and enter the wrestling ring.
Career Milestones
Orpah Winfrey: The Queen of All Media
Winfrey's career breakthrough came in 1986 when she launched "The Oprah Winfrey Show." The show became a cultural phenomenon. drawing millions of viewers daily and earning many awards. Winfrey's empathetic and candid interviewing style resonated with audiences. helping her tackle diverse and often challenging topics.
Beyond her talk show, Winfrey expanded her empire to include the creation of Harpo Productions. a multimedia production company. She also launched "O, The Oprah Magazine" and OWN: Oprah Winfrey Network, further solidifying her status as a media mogul.
Dwayne Johnson: From The Ring to The Big Screen
Dwayne Johnson's wrestling career took off in the late 1990s. when he became one of the most charismatic and popular figures in WWE. His larger-than-life persona and catchphrases endeared him to fans. making him a household name. But, Johnson had ambitions beyond the wrestling ring.
In the early 20
The document summarizes guidelines from the International Commission on Non-Ionizing Radiation Protection (ICNIRP) for limiting exposure to time-varying electric, magnetic, and electromagnetic fields up to 300 GHz. It establishes basic restrictions on exposure levels based on established health effects. It also provides reference levels to help determine if the basic restrictions are exceeded. The guidelines are intended to protect against known adverse health effects from exposure and will be periodically revised as more effects are identified.
This chapter examines analytical and empirical relations used to extract mechanical properties from indentation experiments. Finite element simulations are performed for spherical and conical indentation of elastic, elastic-plastic, and coated materials. The material response is characterized by load-displacement curves. Existing relations for contact area, contact stiffness, and hardness are compared to finite element results. The chapter lays groundwork for using indentation to characterize properties and failure modes of coated materials.
1) Indentation-induced failure of hard coatings is modeled using cohesive surfaces to represent interfacial delamination and coating cracking under normal and shear loads.
2) Results show that shear delamination occurs within the film along a shear plane, while normal delamination separates the film from the substrate.
3) Coating cracking is also observed radially around the indentation with high tensile stresses concentrated at the coating/substrate interface.
The document summarizes a study on modeling fatigue damage in solder interconnects using a cohesive zone approach. Key points:
1) A cohesive zone method is used to model fatigue damage accumulation in solder joints, representing the interface between continuum elements.
2) A damage evolution law based on experimental observations is used to model how damage increases with the number of loading cycles and applied load.
3) Results show the predicted damage distribution in a sample solder joint under cyclic loading, as well as the effects of mean strain and load sequencing on damage accumulation.
This document discusses simulating fatigue damage in solder joints using cohesive zone modeling. It introduces cohesive zone modeling as a numerical method to describe interface mechanics and model crack initiation and propagation. The document proposes using a cohesive zone model with a damage variable to simulate fatigue damage accumulation over successive loading cycles at solder interfaces. The model represents interfaces with cohesive elements having traction-separation laws that degrade nonlinearly based on a damage evolution law to capture fatigue failure below static strength limits.
This study measured environmental radioactivity in Palestine using in situ gamma-ray spectroscopy. Measurements were taken at 18 locations across the West Bank. The detected radionuclides were naturally occurring gamma emitters from 238U, 232Th and 40K decay chains, with 137Cs also identified at a few locations. Activity concentrations ranged from 8-203 Bq/kg for 40K, 6-32 Bq/kg for 238U and 5-30 Bq/kg for 232Th. The total outdoor gamma dose rate was calculated to be 6-30 nGy/h, with an average of 18 ± 7 nGy/h or about 30% of the world average. The results provide a baseline for environmental
This document summarizes a study that models fatigue damage in solder interconnects using a cohesive zone approach. The study simulates fatigue damage over successive loading cycles using finite element analysis. Damage is modeled to occur at interfaces using cohesive zones, which incorporate a damage variable into the constitutive law to account for material degradation over cycles. A damage evolution law is formulated to capture key damage characteristics as damage accumulates. The model predicts solder bump lifetime and shows good agreement with an empirical lifetime model. Damage distribution and stiffness loss are examined over cycles. The analysis is currently limited to 2D but aims to provide a more realistic fatigue simulation than models that assume constant material properties.
This document summarizes a numerical study of indentation-induced cracking in brittle coatings on ductile substrates. Finite element modeling was used to simulate indentation with a spherical indenter. The coating was modeled as linear elastic, the substrate as elastic-perfectly plastic, and cracks in the coating were modeled using cohesive surfaces. Circumferential cracks were found to initiate at the coating surface near the contact edge due to high tensile radial stresses. The first crack caused a kink in the load-displacement curve. The spacing between cracks was on the order of the coating thickness. The effects of material properties and cohesive parameters on crack initiation and spacing were also investigated.
This document summarizes a numerical simulation of indentation-induced delamination of an elastic film on an elastic-plastic substrate. The simulation models the interface between the film and substrate using a cohesive surface that allows for both normal and tangential displacement. It is found that delamination occurs in a tangential mode rather than a normal mode and is initiated at a distance of two to three times the contact radius. The speed of delamination propagation depends on the interfacial strength, with stronger interfaces producing higher initial speeds and lower steady state speeds. Indentation load vs. depth curves may exhibit a "kink" when delamination is initiated for interfaces of relatively high strength.
Unveiling Paul Haggis Shaping Cinema Through Diversity. .pdfkenid14983
Paul Haggis is undoubtedly a visionary filmmaker whose work has not only shaped cinema but has also pushed boundaries when it comes to diversity and representation within the industry. From his thought-provoking scripts to his engaging directorial style, Haggis has become a prominent figure in the world of film.
The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...greendigital
Leonardo DiCaprio, a name synonymous with Hollywood stardom and acting excellence. has captivated audiences for decades with his talent and charisma. But, the Leonardo DiCaprio haircut is one aspect of his public persona that has garnered attention. From his early days as a teenage heartthrob to his current status as a seasoned actor and environmental activist. DiCaprio's hairstyles have evolved. reflecting both his personal growth and the changing trends in fashion. This article delves into the many phases of the Leonardo DiCaprio haircut. exploring its significance and impact on pop culture.
Christian Louboutin: Innovating with Red Solesget joys
Christian Louboutin is celebrated for his innovative approach to footwear design, marked by his trademark red soles. This in-depth look at his life and career explores the origins of his creativity, the milestones in his journey, and the impact of his work on the fashion industry. Learn how Louboutin's bold vision and dedication to excellence have made his brand synonymous with luxury and style.
Everything You Need to Know About IPTV Ireland.pdfXtreame HDTV
The way we consume television has evolved dramatically over the past decade. Internet Protocol Television (IPTV) has emerged as a popular alternative to traditional cable and satellite TV, offering a wide range of channels and on-demand content via the internet. In Ireland, IPTV is rapidly gaining traction, with Xtreame HDTV being one of the prominent providers in the market. This comprehensive guide will delve into everything you need to know about IPTV Ireland, focusing on Xtreame HDTV, its features, benefits, and how it is revolutionizing TV viewing for Irish audiences.
Orpah Winfrey Dwayne Johnson: Titans of Influence and Inspirationgreendigital
Introduction
In the realm of entertainment, few names resonate as Orpah Winfrey Dwayne Johnson. Both figures have carved unique paths in the industry. achieving unparalleled success and becoming iconic symbols of perseverance, resilience, and inspiration. This article delves into the lives, careers. and enduring legacies of Orpah Winfrey Dwayne Johnson. exploring how their journeys intersect and what we can learn from their remarkable stories.
Follow us on: Pinterest
Early Life and Backgrounds
Orpah Winfrey: From Humble Beginnings to Media Mogul
Orpah Winfrey, often known as Oprah due to a misspelling on her birth certificate. was born on January 29, 1954, in Kosciusko, Mississippi. Raised in poverty by her grandmother, Winfrey's early life was marked by hardship and adversity. Despite these challenges. she demonstrated a keen intellect and an early talent for public speaking.
Winfrey's journey to success began with a scholarship to Tennessee State University. where she studied communication. Her first job in media was as a co-anchor for the local evening news in Nashville. This role paved the way for her eventual transition to talk show hosting. where she found her true calling.
Dwayne Johnson: From Wrestling Royalty to Hollywood Superstar
Dwayne Johnson, also known by his ring name "The Rock," was born on May 2, 1972, in Hayward, California. He comes from a family of professional wrestlers, with both his father, Rocky Johnson. and his grandfather, Peter Maivia, being notable figures in the wrestling world. Johnson's early life was spent moving between New Zealand and the United States. experiencing a variety of cultural influences.
Before entering the world of professional wrestling. Johnson had aspirations of becoming a professional football player. He played college football at the University of Miami. where he was part of a national championship team. But, injuries curtailed his football career, leading him to follow in his family's footsteps and enter the wrestling ring.
Career Milestones
Orpah Winfrey: The Queen of All Media
Winfrey's career breakthrough came in 1986 when she launched "The Oprah Winfrey Show." The show became a cultural phenomenon. drawing millions of viewers daily and earning many awards. Winfrey's empathetic and candid interviewing style resonated with audiences. helping her tackle diverse and often challenging topics.
Beyond her talk show, Winfrey expanded her empire to include the creation of Harpo Productions. a multimedia production company. She also launched "O, The Oprah Magazine" and OWN: Oprah Winfrey Network, further solidifying her status as a media mogul.
Dwayne Johnson: From The Ring to The Big Screen
Dwayne Johnson's wrestling career took off in the late 1990s. when he became one of the most charismatic and popular figures in WWE. His larger-than-life persona and catchphrases endeared him to fans. making him a household name. But, Johnson had ambitions beyond the wrestling ring.
In the early 20
The Unbelievable Tale of Dwayne Johnson Kidnapping: A Riveting Sagagreendigital
Introduction
The notion of Dwayne Johnson kidnapping seems straight out of a Hollywood thriller. Dwayne "The Rock" Johnson, known for his larger-than-life persona, immense popularity. and action-packed filmography, is the last person anyone would envision being a victim of kidnapping. Yet, the bizarre and riveting tale of such an incident, filled with twists and turns. has captured the imagination of many. In this article, we delve into the intricate details of this astonishing event. exploring every aspect, from the dramatic rescue operation to the aftermath and the lessons learned.
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The Origins of the Dwayne Johnson Kidnapping Saga
Dwayne Johnson: A Brief Background
Before discussing the specifics of the kidnapping. it is crucial to understand who Dwayne Johnson is and why his kidnapping would be so significant. Born May 2, 1972, Dwayne Douglas Johnson is an American actor, producer, businessman. and former professional wrestler. Known by his ring name, "The Rock," he gained fame in the World Wrestling Federation (WWF, now WWE) before transitioning to a successful career in Hollywood.
Johnson's filmography includes blockbuster hits such as "The Fast and the Furious" series, "Jumanji," "Moana," and "San Andreas." His charismatic personality, impressive physique. and action-star status have made him a beloved figure worldwide. Thus, the news of his kidnapping would send shockwaves across the globe.
Setting the Scene: The Day of the Kidnapping
The incident of Dwayne Johnson's kidnapping began on an ordinary day. Johnson was filming his latest high-octane action film set to break box office records. The location was a remote yet scenic area. chosen for its rugged terrain and breathtaking vistas. perfect for the film's climactic scenes.
But, beneath the veneer of normalcy, a sinister plot was unfolding. Unbeknownst to Johnson and his team, a group of criminals had planned his abduction. hoping to leverage his celebrity status for a hefty ransom. The stage was set for an event that would soon dominate worldwide headlines and social media feeds.
The Abduction: Unfolding the Dwayne Johnson Kidnapping
The Moment of Capture
On the day of the kidnapping, everything seemed to be proceeding as usual on set. Johnson and his co-stars and crew were engrossed in shooting a particularly demanding scene. As the day wore on, the production team took a short break. providing the kidnappers with the perfect opportunity to strike.
The abduction was executed with military precision. A group of masked men, armed and organized, infiltrated the set. They created chaos, taking advantage of the confusion to isolate Johnson. Johnson was outnumbered and caught off guard despite his formidable strength and fighting skills. The kidnappers overpowered him, bundled him into a waiting vehicle. and sped away, leaving everyone on set in a state of shock and disbelief.
The Immediate Aftermath
The immediate aftermath of the Dwayne Johnson kidnappin
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Delamination of thin strong film - poster
1. Delamination of a Strong Thin Film From a Ductile Substrate
During Indentation Loading and Unloading
Adnan Abdul-Baqi & Erik van der Giessen
Koiter Institute Delft
Introduction The cohesive surface model
Indentation loading and unloading of a strong elastic In the description of the interface as a cohesive surface, a small dis-
film on a ductile substrate is modeled. The film is con- placement jump ∆ between the film and substrate is allowed, with nor-
sidered to be elastic, the substrate is elastic perfectly- mal and tangential components ∆ n and ∆ t respectively. The
plastic and the indenter is spherical and rigid (Fig. 1). corresponding tractions we adopt in this study are those used by Xu and
The interface is modeled by means of a cohesive surface. Needleman [1]. Figure 2 shows these tractions in their uncoupled form.
˙
h 1.5 3
∆t = 0
1 2 ∆n = 0
R 0.5
1
a 0
t max
max
increasing ∆ t 0
T /τ
−0.5
T /σ
h
n
coating t −1 −1
increasing ∆ n
−1.5
interface (a) −2
(b)
−2
substrate −2.5
−1 0 1 2 3 4 5 6
−3
−3 −2 −1 0 1 2 3
∆n/δn ∆t/δt
Figure 1. Geometry. Figure 2. (a) Normal traction versus normal separation. (b) Tangential traction versus tangential separation.
Results
0.00 σe/σy 0.00 σyy/σmax 2
0.5
φ (J/m2)
1.40
1.0 n
1.26
0.4 a
1.11 0.8 1.75 a 150
0.02 0.97 0.01 0.5 0.3 b b 200
0.82
0.3 c 400
0.68 1.5 0.2
0.53 0.1 c d 600
0.39 -0.1 0.1 e >> 600
0.04 0.24 0.02 1.25 d e
-0.4 0
z (mm)
0.10 1 1.15 1.3 1.45 1.6 1.75
z (mm)
-0.6
F/(πR σy)
2
1
0.06 0.03
0.75
0.5
0.08 0.04
(a) (b) 0.25
0.10 0.05
0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.01 0.02 0.03 0.04 0.05 0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
r (mm) r (mm) h/t
Figure 3. (a) Contour plot of the Von Mises effective stress at the maximum indentation depth
Figure 4. Load versus displacement curves for dif-
( h max = 2t ), φ n = 150 ( J ⁄ m 2 ). Arrows show the shear direction, line shows the location of the tan-
ferent values of interfacial energies. Curve (e) repre-
gentially delaminated area. (b) Contour plot of the vertical stress component at the end of the unloading
sents the case of a perfect interface.
stage ( F = 0 ), φ n = 500 ( J ⁄ m 2 ).
1
Conclusions
0.8
1. For relatively weak interfaces, delamination occurs in the loading stage. It is
0.6 E imprinted on the load vs displacement curve by a ‘kink’.
E/Emax
el
E
pl
E
int
0.4
∫ F dh 2. Normal delamination occurs during the unloading stage, where a circular part
E + E +E
el pl int
0.2
of the coating is lifted off from the substrate. It is imprinted on the load vs dis-
placement curve by a ‘hump’.
0
0 0.5 1 1.5 2
h/t
Figure 5. Evolution of elastic, plastic, interfacial and
applied work during the loading and unloading process. [1] X.-P. Xu, A. Needleman, Model. Simul. Mater. Sci. Eng. 1 (1993) 111.